A two-scale multi-physics deep learning model for smart MEMS sensors

Smart materials and structures, especially those bio-inspired, are often characterized by a hierarchy of length-scales and, accordingly, time-scales. Smart Micro Electro-Mechanical Systems (MEMS), either used as sensors or actuators, are on their own characterized by different physical phenomena affecting their properties at different scales. Data-driven formulations can then be helpful to deal with the complexity of the multi-physics governing their response to the external stimuli, and optimize their performances. As a concrete example, Lorentz force micro-magnetometers can be adopted for navigation purposes, thanks to the interaction of the Earth magnetic field with a current flowing inside a semiconducting, micro-structured medium. If an alternating current with an ad-hoc set frequency is let to flow longitudinally in a slender mechanical part, or beam, the system is driven into resonance and the sensitivity to the magnetic field to be sensed may result largely enhanced. In our former research activity, a single-axis Lorentz force MEMS magnetometer with a simple geometry was proposed, validated and fabricated; a reduced-order physical model of its movable structure was also developed, to feed a multi-physics and multi-objective topology optimization procedure. This model-based approach did not account for stochastic effects, which lead to the scattering in the experimentally acquired data at such micrometric length-scale. The formulation is here improved to allow for such stochastic effects through a 2-scale deep learning model designed as follows: at the material scale, a deep neural network is adopted to learn the scattering in the mechanical properties of polysilicon induced by its (poly)crystalline morphology; at the device scale, a physical model is adopted to account for the effects of scattering in the environment-driven etch defects on the overall response of the device; still at the device scale, a further deep neural network is adopted to learn the most important geometric features of the movable parts that affect the overall performance of the magnetometer. Some preliminary results are discussed, and the extension to more complex geometries is finally foreseen