Direct inference of parameters for piezoresistive micromechanical resonators embedded in feedthrough

• Published in: Sensors and actuators. A. Physical. 2012-10, Vol.186, p.257-263
• Main Authors: Lee, Joshua E.-Y., Xu, Yuanjie
• Format: Article
• Language: English
• Subjects: Actuators; Extraction; Feedthrough; Inference; Mathematical models; MEMS; Motional; Noise levels; Piezoresistive; Quality factor; Resonators
• ISSN: 0924-4247; 1873-3069
• DOI: 10.1016/j.sna.2012.03.043

► Method/approach to directly infer all the parameters for a piezoresistive resonator that is heavily embedded in parasitic capacitive feedthrough. ► Such capability is being demonstrated for the first time. ► Given its efficiency for parameter extraction/estimation, this paper demonstrates that differences with more detailed extraction procedures are within 5% ► Limits of this approach when feedthrough is extremely large are highlighted within. ► Given the interest in MEMS resonators which are basic components in many MEMS applications and the use of the piezoresistive effect for enhanced characterization, the proposed tool will be of much interest. This paper reports a means of directly inferring all the characteristic lumped parameters (including the quality factor) for a piezoresistive micromechanical resonator with an electrical transmission heavily buried in parasitic capacitive feedthrough. This is particularly useful when the height of the resonant peak is less than 3dB such that the quality factor cannot be directly obtained. In this limit, the magnitude of the resonance is comprised mainly of the feedthrough contribution and hence unrepresentative of the motional output from the resonator. To validate the accuracy of this method of parameter inference, we have applied the method to electrical transmission measurements for an electrostatically actuated square-extensional bulk mode resonator whose motional current is sensed piezoresistively. Due to substantial feedthrough, the height of the resonant peak is less than 0.22dB such that the quality factor cannot be obtained through the −3dB bandwidth since this information is not directly available. The values of parameters estimated using the reported method compare well (to within 5%) with those obtained by a more protracted and accurate extraction procedure that involves the subtraction of the modeled feedthrough contribution from the measured data followed by a model curve fit.