Uncertainty quantification in polysilicon MEMS through on-chip testing and reduced-order modelling

Abstract

In this paper, micro-scale uncertainties affecting the behaviour of microelectromechanical systems (MEMS) are investigated through a mixed numerical/experimental approach. An on-chip test device has been designed and fabricated using standard MEMS fabrication techniques, to deform a (microstructured) polysilicon beam. To interpret the experimental data and also the relevant scatterings in the system response, a high fidelity, parametric finite element (FE) model of the device is developed in ANSYS. Uncertainties in the parameters governing the polysilicon mechanical properties and the geometry of the movable structure are estimated through an inverse analysis. To systematically quantify the uncertainty levels within the realm of a cost-effective statistical analysis, a model order reduction technique based on a synergy of proper orthogonal decomposition (POD) and Kriging interpolation is proposed. The resulting reduced order model is finally fed into a transitional Markov chain Monte Carlo (TMCMC) algorithm for the estimation of the unknown parameters.