A force sensor based on three weakly coupled resonators with ultrahigh sensitivity, Sensors & Actuators: A. Physical (2015), http://dx.doi.org/10.1016/j.sna. 2015.05.011 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. AbstractA proof-of-concept force sensor based on three degree-of-freedom (DoF) weakly coupled resonators was fabricated using a silicon-on-insulator (SOI) process and electrically tested in 20µTorr vacuum. Compared to the conventional single resonator force sensor with frequency shift as output, by measuring the amplitude ratio of two of the three resonators, the measured force sensitivity of the 3DoF sensor was 4.9 × 10 6 /N, which was improved by two orders magnitude. A bias stiffness perturbation was applied to avoid mode aliasing effect and improve the linearity of the sensor. The noise floor of the amplitude ratio output of the sensor was theoretically analyzed for the first time, using the transfer function model of the 3DoF weakly coupled resonator system. It was shown based on measurement results that the output noise was mainly due to the thermalelectrical noise of the interface electronics. The output noise spectral density was measured, and agreed well with theoretical estimations. The noise floor of the force sensor output was estimated to be approximately 1.39nN for an assumed 10Hz bandwidth of the output signal, resulting in a dynamic range of 74.8dB.

This paperreports a three degree-offreedom (3DoF) microelectromechanical systems (MEMS) resonant sensing device consisting of three weakly coupled resonators with enhanced sensitivity to stiffness change. If one resonator of the system is perturbed by an external stimulus, mode localization occurs, which can be detected by a change of modal amplitude ratio. The perturbation can be, for example, a change in stiffness of one resonator. A detailed theoretical investigation revealed that a mode aliasing effect, along with the thermal noise floor of the sensor and the associated electrical system ultimately limit the dynamic range of the sensor. The nonlinearity of the 3DoF sensor was also analyzed theoretically. The 3DoF resonator device was fabricated using a silicon on insulator process. Measurement results from a prototype device agreed well with the predictions of the analytical model. A significant, namely 49 times, improvement in sensitivity to stiffness change was evident from the fabricated 3DoF resonator sensor compared with the existing state-of-the-art 2DoF resonator sensors, while the typical nonlinearity was smaller than ±2% for a wide span of stiffness change. In addition, measurements indicate that a dynamic range of at least 39.1 dB is achievable, which could be further extended by decreasing the noise of the device and the interface electronics.[2015-0020] Index Terms-Microelectromechanical systems (MEMS) resonator, stiffness change sensor, dynamic range, nonlinearity, three degree-of-freedom. I. INTRODUCTIONO VER THE last couple of decades, micro-and nanofabricated resonant devices have been widely used to sense small changes in the properties of the resonator [1], namely the stiffness [2] and mass [3] of the resonator. Among these, sensing devices that detect stiffness change have been Manuscript

This paper systematically investigates the characteristics of different output metrics for a weakly coupled three degree-of-freedom microelectromechanical systems resonant sensor. The key figures-of-merit examined are sensitivity and linear range. The four main output metrics investigated are mode frequency shift, amplitude difference, amplitude ratio, and eigenstate shift. It is shown from theoretical considerations, equivalent RLC circuit model simulations and electrical measurements, that there is a strong tradeoff between sensitivity and linear range. For instance, the amplitude difference has the best sensitivity but the worst linear range, whereas frequency shift has the widest linear range but the lowest sensitivity. We also show that using the vibrational amplitude ratio as an output metric provides the best balance between sensitivity and linear range. [2016-0077]Index Terms-Output metrics, frequency shift, amplitudebased output signals, weakly coupled microelectromechanical systems (MEMS) resonant sensors.

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