A Stochastic Model to Describe the Scattering in the Response of Polysilicon MEMS

Abstract

The current miniaturization trend in the market of inertial microsystems is leading to movable device parts with sizes comparable to the characteristic length-scale of the polycrystalline silicon film morphology. The relevant output of micro electro-mechanical systems (MEMS) is thus more and more affected by a scattering, induced by features resulting from the micro-fabrication process. We recently proposed an on-chip testing device, specifically designed to enhance the aforementioned scattering in compliance with fabrication constraints. We proved that the experimentally measured scattering cannot be described by allowing only for the morphology-affected mechanical properties of the silicon films, and etch defects must be properly accounted for too. In this work, we discuss a fully stochastic framework allowing for the local fluctuations of the stiffness and of the etch-affected geometry of the silicon film. The provided semi-analytical solution is shown to catch efficiently the measured scattering in the C-V plots collected through the test structure. This approach opens up the possibility to learn on-line specific features of the devices, and to reduce the time required for their calibration.

Two-Scale Deep Learning Model for Polysilicon MEMS Sensors

“…For the particular case of polysilicon-based MEMS, two main sources of uncertainty have been observed to intensify with the miniaturization of the devices [22][23][24][25][26][27]. The first source is related to the limits of the production process, i.e., when the size of the MEMS is in the same order of magnitude of the tolerances established by the microfabrication process.…”

“…We consider the Lorentz force MEMS magnetometer introduced in [20,21], and propose a new formulation resting on a two-scale deep learning model designed as follows: at the material level, a deep neural network is used a priori to learn the scattering in the mechanical properties of polysilicon induced by its morphology; at the device level, a further deep neural network is used to account for the effects on the response induced by etch defects, learning on-the-fly relevant geometric features of the movable parts. Hence, material-and geometry-related uncertainty sources, whose effects have been formerly studied and observed to intensify with the reduction in the size [22][23][24][25][26][27], are accounted for in this formulation. In concrete terms, the response is characterized in terms of the maximum oscillation amplitude of the resonant structure, a significant design parameter due to its direct relation with relevant figures of merit of the entire device, such as the responsivity and resolution [28].…”

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

“…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.…”