On-Chip Assessment of Scattering in the Response of Si-Based Microdevices

The response of micromachines to the external actions is typically affected by a scattering, which is, on its own, induced by their microstructure and by stages of the microfabrication process. The progressive reduction in size of the mechanical components, forced by a path towards (further) miniaturization, has recently enhanced the outcomes of the aforementioned scattering, and provided a burst in research activities to address issues linked to its assessment. In this work, we discuss the features of an on-chip testing device that we purposely designed to efficiently estimate the two major sources of scattering affecting inertial, polysilicon-based micromachines: the morphology of the silicon film constituting the movable parts of the device, and the etch defect or over-etch induced by microfabrication. The coupled electro-mechanical behavior of the statically determinate movable (micro)structure of the on-chip device has been modeled via beam bending theory, within which the aforementioned sources of scattering have been accounted for through local fluctuating fields in the compliant part of the structure itself, namely the supporting spring. The proposed stochastic model is shown to outperform former ones available in the literature, which neglected the simultaneous and interacting effects of the two mentioned sources on the measure response. The model can fully catch the scattering in the C–V plots up to pull-in, hence, also in the nonlinear working regime of the device.

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

Engineering Proceedings ◽

10.3390/engproc2020002095 ◽

2021 ◽

Vol 2 (1) ◽

pp. 95

Author(s):

Luca Dassi ◽

Marco Merola ◽

Eleonora Riva ◽

Angelo Santalucia ◽

Andrea Venturelli ◽

...

Keyword(s):

Silicon Film ◽

Micro Fabrication ◽

Micro Electro Mechanical Systems ◽

Local Fluctuations ◽

Stochastic Framework ◽

On Line ◽

Chip Testing ◽

On Chip ◽

Time Required ◽

Polycrystalline Silicon Film

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.

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