Data-driven stochastic models for spatial uncertainties in micromechanical systems

Accurate uncertainty quantification in engineering systems requires the use of proper data-driven stochastic models that bear a good fidelity with respect to experimentally observed variations. This paper looks at a variety of modeling techniques to represent spatially varying uncertainties in a form that can be incorporated into numerical simulations. In the context of microelectromechanical systems, we consider spatial uncertainties at the device level in the form of surface roughness and at the wafer level in the form of non-uniformities that arise as a result of various microfabrication steps. We discuss methods to obtain roughness characterization data ranging from the use of a simple profilometer probe to imaging-based techniques for the extraction of digitized data from images. We model spatial uncertainties as second-order stochastic process and use Bayesian inference to estimate the model parameters from the input data. We apply the data-driven stochastic models generated from this process to micromechanical actuators and sensors in which these spatial uncertainties are likely to cause significant variation. These include an electrostatically-actuated torsion-spring micromirror, an electromechanical comb-drive actuator and a pressure sensor with a piezoresistive strain gauge. We show that the performance of these devices is sensitive to the presence of spatial uncertainties and a proper modeling of these uncertainties helps us make reliable predictions about the variation in device performance. Where data is available, we even show that the predicted variation can be validated against experimental observations, highlighting the significance of proper stochastic modeling in the analysis of such devices.