Frequency adjustment of microelectromechanical cantilevers using electrostatic pull down

Abstract

In this paper, a new way of actively tuning the resonant frequency of vibrating microelectromechanical devices by electrostatically adjusting the length of the resonating structure is explored. Variations in micromachining processes cause submicron differences in the size of fabricated micromachined devices, which lead to frequency variations in resonators. For radio frequency (RF) applications where high frequency selectivity and low noise frequency manipulation are key performance issues, micromachined resonators need to output a fixed frequency if they are to replace current off-chip, passive devices. This motivates the investigation of post-fabrication techniques that compensate for fabrication defects and errors, and shift the resonant frequency to its designed value. A simple universal analytical model has been developed to investigate the different states a cantilever undergoes during pull-in due to an applied voltage. The beam's natural frequencies throughout these states have been plotted. It is shown that the frequency can be changed by a factor of 4 during pull down, and thereafter increased proportionally with actuation provided an initial minimum voltage was applied.

Tunable Micro- and Nanomechanical Resonators

“…Active tuning is defined as a tuning mechanism that is continuously applied even if the resonant frequency closely matches the excitation vibration frequency [ 37 ]. Real time tuning makes these methods very attractive and some active methods, including electrothermal [ 14 , 19 ], electrostatic [ 38 , 39 , 40 ], magnetomotive [ 41 ], piezoelectrical [ 42 , 43 ], dielectric [ 44 ], photothermal [ 45 ], and modal coupling [ 46 , 47 ], as well as the tension-induced tuning mechanisms, have been developed and reported. In contrast, passive tuning method often operates periodically and only consumes power during the tuning operation [ 37 ].…”

Mass Detection in Viscous Fluid Utilizing Vibrating Micro- and Nanomechanical Mass Sensors under Applied Axial Tensile Force

“…To begin, we recall the known fact that flexural oscillations of the majority of micro-/ nanosized beams, including those used as mass sensors, are realized and controlled by an external electrical or electromagnetic field, which creates a constant axial force [ 5 , 17 , 35 , 36 , 37 , 38 ]. In order to verify the practicality of the proposed technique, the suspended multi-walled carbon nanotube-based mass sensor (MWCNT) of density 2.1 g/cm 3 , elastic moduli 1.15 TPa, and of length 11.4 μm with outer and innermost diameters of 15 nm and 3 nm, respectively, which is loaded by a mass of m = 122 ag, i.e.…”

An experimental analysis of electrostatically vibrated array of polysilicon cantilevers

“…Ladabaum et al (1998) and Chowdhury et al (2005) have presented the effective spring constant of the electrostatically actuated structures. Thorough investigation of dynamic change in frequency due to non-linear effects of electrostatic actuation has been carried out by Kafumbe et al (2005) and Alsaleem et al (2009). However, if the amplitude of the voltage V 0 is kept very small, much smaller than the pull-in voltage of the beam, the steady deflection and hence static spring softening can be ignored.…”