Physically-Based Reduced Order Modelling of a Uni-Axial Polysilicon MEMS Accelerometer

Aldo Ghisi,Stefano Mariani,Sarah Zerbini,Alberto Corigliano

doi:10.3390/s121013985

Aldo Ghisi, Stefano Mariani + Show 2 more

Open Access

https://doi.org/10.3390/s121013985

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Abstract

In this paper, the mechanical response of a commercial off-the-shelf, uni-axial polysilicon MEMS accelerometer subject to drops is numerically investigated. To speed up the calculations, a simplified physically-based (beams and plate), two degrees of freedom model of the movable parts of the sensor is adopted. The capability and the accuracy of the model are assessed against three-dimensional finite element simulations, and against outcomes of experiments on instrumented samples. It is shown that the reduced order model provides accurate outcomes as for the system dynamics. To also get rather accurate results in terms of stress fields within regions that are prone to fail upon high-g shocks, a correction factor is proposed by accounting for the local stress amplification induced by re-entrant corners.

Highlights

Several attempts to provide efficient, robust and accurate reduced order models (ROMs) for nonlinear systems, with a specific focus on MEMS, have been recently published
We showed that the model is capable of matching the actual MEMS dynamics, but we did not discuss its accuracy at varying maximum acceleration levels under guided or free falls and the computational gain with respect to finite element (FE) simulations
The ROM accuracy and performance are assessed against FE simulations and available experimental data. Both the ROM and the FE model are fed by the input acceleration loadings depicted in Figure 3, already considered in [32]

Summary

Introduction

Several attempts to provide efficient, robust and accurate (or, at least, informative) reduced order models (ROMs) for nonlinear systems, with a specific focus on MEMS, have been recently published. Based ROMs of the mechanical behaviour of microsystems were instead presented in [18,19] In these papers, instead of considering the problem in an abstract way and operating through mathematical tools to project the system dynamics onto subspaces of the actual evolution one, the mechanics of the movable parts of the sensors as well as the effect of external actions on them were taken account of. At the macro-scale the focus is on the propagation of stress waves inside the package; at the meso-scale the focus is instead on the dynamics of the movable parts of the whole MEMS; eventually, at the micro-scale the degradation of the mechanical properties of the polysilicon film, and the resulting failure mechanism are simulated While this three-scale approach proved accurate and allowed us to match unexpected effects linked to the package in case of drops [29], it turned out to be time-consuming.

Reduced Order Modelling of a Uni-Axial MEMS Accelerometer

Results

Conclusions