Figure of Merit Enhancement of Laterally Vibrating RF-MEMS Resonators via Energy-Preserving Addendum Frame

This paper examines a new technique to improve the figure of merit of laterally vibrating RF-MEMS resonators through an energy-preserving suspended addendum frame structure using finite element analysis. The proposed suspended addendum frame on the sides of the resonant plate helps as a mechanical vibration isolator from the supporting substrate. This enables the resonator to have a low acoustic energy loss, resulting in a higher quality factor. The simulated attenuation characteristics of the suspended addendum frame are up to an order of magnitude larger than those achieved with the conventional structure. Even though the deployed technique does not have a significant impact on increasing the effective electromechanical coupling coefficient, due to a gigantic improvement in the unloaded quality factor, from 4106 to 51,136, the resonator with the suspended frame achieved an 11-folds improvement in the figure of merit compared to that of the conventional resonator. Moreover, the insertion loss was improved from 5 dB down to a value as low as 0.7 dB. Furthermore, a method of suppressing spurious mode is demonstrated to remove the one incurred by the reflected waves due to the proposed energy-preserving structure.

Applied Mechatronics: On Mitigating Disturbance Effects in MEMS Resonators Using Robust Nonsingular Terminal Sliding Mode Controllers

This investigation attempts to study a possible controller in improving the dynamic stability of capacitive microstructures through mitigating the effects of disturbances and uncertainties in their resultant dynamic behavior. Consequently, a nonsingular terminal sliding mode control strategy is suggested in this regard. The main features of this particular control strategy are its high response speed and its non-reliance on powerful controller forces. The stability of the controller was investigated using Lyapunov theory. For this purpose, a suitable Lyapunov function was introduced to prove the stability of a controller, and the singularity conditions and methods to overcome these conditions are presented. The achieved results proved the high capability of the applied technique in stabilizing of the microstructure as well as mitigating the effects of disturbances and uncertainties.

Dynamic behaviours of the Double-end tuning fork based comb-driven microelectromechanical resonators for modulating the magnetic flux synchronously

MEMS resonators have been widely used in the magneto-resistive (MR) sensor for modulating the magnetic flux to enhance the detection limit. However, the manufacturing tolerances in MEMS fabrication processes make it challenging to fabricate the identical resonators with the same vibration frequency, which greatly decreases the detection limit of the MR sensor. To synchronize the MEMS resonators and improve the performance of the MR sensor, the double end tuning fork (DETF) based comb-driven MEMS resonators is proposed in this paper, making the system operate at the out-of-phase mode to complete the synchronization. The dynamic behaviour of the resonators is investigated through theoretical analysis, numerical solution based on MATLAB code and Simulink, and experimental verification. The results show that the transverse capacitances in the comb will significantly affect the resonance frequency due to the second-order electrostatic spring constant. It is the first time to observe the phenomenon that the resonant frequency increases with the increase of the bias, and it can also decrease with increasing the bias through adjusting the initial space between the fixed finger and the moving mass, they are different from the model about spring softening and spring hardening. Besides, the proposed DETF-based comb-driven resonators can suppress the in-phase and out-of-phase mode through adjusting the driving and sensing ports, and sensing method, meanwhile make the magnetic flux modulation fully synchronized, and maximize the modulation efficiency, and minimize the detection limit. These characteristics are appropriate for the MR sensor, even other devices that need to adjust the resonance frequency and vibration amplitude. Furthermore, the model and the design can also be extended to characteristic the single end tuning fork (SETF) based MEMS resonator and other MEMS-based MR sensors.

Controlling Resonator Nonlinearities and Modes through Geometry Optimization

Controlling the nonlinearities of MEMS resonators is critical for their successful implementation in a wide range of sensing, signal conditioning, and filtering applications. Here, we utilize a passive technique based on geometry optimization to control the nonlinearities and the dynamical response of MEMS resonators. Also, we explored active technique i.e., tuning the axial stress of the resonator. To achieve this, we propose a new hybrid shape combining a straight and initially curved microbeam. The Galerkin method is employed to solve the beam equation and study the effect of the different design parameters on the ratios of the frequencies and the nonlinearities of the structure. We show by adequately selecting the parameters of the structure; we can realize systems with strong quadratic or cubic effective nonlinearities. Also, we investigate the resonator shape effect on symmetry breaking and study different linear coupling phenomena: crossing, veering, and mode hybridization. We demonstrate the possibility of tuning the frequencies of the different modes of vibrations to achieve commensurate ratios necessary for activating internal resonance. The proposed method is simple in principle, easy to fabricate, and offers a wide range of controllability on the sensor nonlinearities and response.

INVESTIGATION ON EFFECT OF SURFACE ROUGHNESS PATTERN TO DYNAMIC PERFORMANCE OF MEMS RESONATORS IN VARIOUS TYPES OF GASES AND GAS RAREFACTION

The average modified molecular gas lubrication (MMGL) equation, which is modified with pressure flow factors and effective viscosity, is utilized to analyze the squeeze film damping (SFD) on micro-beam resonators considering effect of surface roughness pattern in various types of gases and gas rarefaction. Then, effect of surface roughness pattern (film thickness ratio and Peklenik number) is discussed on the quality factor (Q-factor) of micro-beam resonators in various types of gases and gas rarefaction. Thus, effect of surface roughness pattern is significantly reduced as effective viscosity of gas decreases in higher mode of resonator and higher gas rarefaction.

Fabrication and Resonance Characteristics of PZT Cantilevers

Thin films of lead zirconate titanate Pb(Zr0,52Ti0,48)O3 (PZT) with thickness of 1.4 μm were prepared on Si/SiO2/TiO2/Pt substrates by chemical solutions deposition. Based on the obtained films, the structures of PZT cantilevers were formed, with a length from 500 to 1000 /um and wide from 100 to 500 μm. Platinum (100 nm) as the bottom and top electrode, has been deposited by magnetron sputtering. PZT cantilevers werereleased by etching the sacrificial layer in SF6. The resonance characteristics of the PZT cantilevers were determined by the light lever method using a special optical measuring stand. Output characteristics of the PZT cantilevers, can be used in MEMS devices, specially, in MEMS resonators.

Geometry Optimization for Resonator Nonlinearities and Modes Controlling

In this paper, we utilize a passive technique based on geometry optimization to control the nonlinearities and the dynamical response of MEMS resonators. To achieve this, we propose a new hybrid shape combining a straight and initially curved microbeam. The Galerkin method is employed to solve the beam equation and study the effect of the different design parameters on the ratios of the frequencies and the nonlinearities of the structure. We show by adequately selecting the parameters of the structure; we can realize systems with strong quadratic or cubic nonlinearities or even zero nonlinearity. Also, we investigate the resonator shape effect on breaking the symmetry and explore different linear coupling phenomena: crossing, veering, and mode hybridization. We demonstrate the possibility of controlling the frequencies of the different modes of vibrations to achieve commensurate ratios necessary for activating internal resonance. The ability to activate the nonlinearities and tuning the frequencies is essential for wide range of applications in signal filtering, sensing, timing, and mass and gas sensing. The proposed method is simple in principle, easy to fabricate, and offers a wide range of controllability on the sensor nonlinearities and response. In addition, the passive techniques does not need additional circuits, to control the frequencies, which help reducing the device size, cost, and power consumption.