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.

A Two-Scale Multi-Physics Deep Learning Model for Smart MEMS Sensors

“…Here, in terms of effective values: m is the mass of the beam and of the attached plates; d is the damping coefficient; 1 K and 3 K are, respectively, the Figure 1. SEM picture of the movable structure of the resonant MEMS magnetometer [16].…”

“…In this work, we propose a two-scale ML approach based on an assembly of ANNs (CNNs and MLPs) at different length-scales, to provide an accurate property-performance mapping for polysilicon MEMS devices. We specifically focus on a single-axis Lorentz force magnetometer introduced in [15] [16]. Material-and geometry-related uncertainty sources, whose effects have been observed to get enhanced as the device footprint is reduces [17]- [22], are addressed independently at the two scales: first, at the material (micro) scale, the effects of the morphology of the film constituting the movable structure are learned; next, at the device (meso) scale, the effects of the microfabrication process and of the geometry of the device are accounted for and learned on their own.…”

“…A surrogate model is accordingly proposed, with the capability of an automatic detection of the effects of the uncertainty causes encoded in the output of the MEMS device, finally leading to an accurate one-to-one input-output mapping. As a further technical aspect, the ground-truth data used for training, validation and testing of the proposed ANN-based model have been obtained via a reduced-order model of the entire device discussed in [15] [16].…”

Effect of Imperfections Due to Material Heterogeneity on the Offset of Polysilicon MEMS Structures

“…The graphs in Figure 12 include, as a reference, the previous curves for FE and analytical results related to the effects due to the scattering of Young’s modulus only: the scattering due to a variable moment of inertia was shown to be far larger, as evidenced by the lower slope of the dashed orange curve and by the corresponding standard deviation, which increased from 2.5–8.2 μm, while the mean value was about zero in all cases. Two additional curves, in blue lines, were also added to the graph: they represent the scattering of the offset, due to the uncertainty on the material only, when the two springs in Figure 1 differed in width exactly by a value of 150 nm, which is representative of the 95% confidence interval from the target during the manufacturing process [12,43]. It can be seen that most of the offsets fell within the range dictated by the two blue curves.…”

Stochastic Mechanical Characterization of Polysilicon MEMS: A Deep Learning Approach

“…Paths toward further miniaturization for semiconductor technologies may pose issues in the prediction of the relevant performances of micro-devices like micro-electro-mechanical systems MEMS [1][2][3]. Usually, the geometrical and physical properties of the devices are assumed to be known in a deterministic sense; in reality, uncertainties are unavoidable and may become dominant as a result of the micro-fabrication process [4][5][6][7].…”