Analysis of vibration modes in a micromechanical square-plate resonator

Vibration modes of a micromechanical square-plate resonator were studied using a scanning laser interferometer. The resonator consists of a square plate released from a silicon substrate and has its main resonance at 13.1 MHz. The resonator is designed to utilize a square-extensional vibration mode in which the vibrations mainly take place in the direction parallel to the surface of the plate. A special detection scheme was used to allow measurement of the in-plane vibrations in addition to the out-of-plane component detected by the interferometer. The measured vibration modes were compared to numerical finite-element simulations with good agreement. In particular, it was found out that the out-of-plane vibration field measured at the resonance frequency of the main mode is a superposition of a parasitic vertical vibration mode and the out-of-plane component of the main mode. Furthermore, the measurements revealed undesirable vibrations in the anchor regions indicating energy leakage from the resonator causing additional losses. The quality factors of the vibration modes were also determined from the laser-probe measurements and they agree quite well with those determined from electrical measurements.