Study of the nonlinearities in micromechanical clamped-clamped beam resonators using stroboscopic SEM

This paper presents a comprehensive study of the nonlinearities in micromechanical clamped-clamped beam resonators using a stroboscopic scanning electron microscopy (SEM) technique. Stroboscopic SEM allows direct imaging and measurement of the resonator's momentary displacement, hence eliminating the uncertainties associated with the conventional characterization methods. Five different silicon-on-insulator (SOI) comb-drive clamped-clamped beam resonators with resonant frequencies ranging from 113 kHz to 239 kHz were designed, fabricated and tested to investigate how their nonlinearities are related to the device dimensions. Both the theoretical analysis and experimental results conclusively show that the critical vibration amplitude of the resonator is around 1% of the beam width in a vacuum and is relatively independent of the beam length. Furthermore, it is found that the maximum storable energy of the resonator can be significantly increased by increasing the beam width and/or reducing the beam length if there are no restrictions on these dimensions. On the other hand, if a specific resonant frequency needs to be maintained, the maximum storable energy can be improved by increasing both the beam width and length by the same factor. Such a study not only helps to reveal the intrinsic nonlinear properties of the micromechanical clamped-clamped beam resonators, but also provides useful design guidelines for engineers to optimize the overall device performance.