Determination of Parameters With Uncertainties for Quality Control in MEMS Fabrication

Abstract

A reliable technique for rapid monitoring of critical dimensional and material parameters during the fabrication of microelectromechanical systems (MEMS) is still an open task. Electrical excitation is sometimes simply not possible, or an electrical test does not reveal sufficient information for a complete characterization. In this paper, we present a new approach that employs optical testing of MEMS vibration frequencies. It is not necessary to have electrical connections because we have developed probes with transparent electrodes to excite vibrations electrostatically without contact on the wafer level. Broadbandwidth excitation is applied to detect all relevant resonances interferometrically through the probes in a single broad-band measurement. Peak detection of the resonances results in a measurement vector containing the resonant frequencies. We demonstrate a new method to estimate system parameters by model identification. The analytical models are derived from a general approach based on finite-element analysis. The parameters with uncertainties are finally determined by guaranteed parameter estimation.[2012-0315]

Nonlinear tuning of microresonators for dynamic range enhancement

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“…Here, we solve for φ (2) n , φ (3) n and φ (4) n using the method of variation of parameters in terms of the basis functions…”

“…We make the choices of φ (3) n and φ (4) n unique (cf. [46]) by setting the initial condition for the coefficient functions for β 4 to 0.…”

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Optical three-dimensional vibrometer microscope with picometer-resolution in x, y, and z

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