A coupled-mode analysis of mode localization on weakly-coupled silicon micromechanical resonators with damping

Mode localization on weakly-coupled silicon resonators in the areas of microelectromechanical systems (MEMS) has been widely studied for highly sensitive sensors of physical and chemical parameter monitoring. In terms of its operation principle, i.e., energy conservation, a system for the weakly-coupled silicon resonator is required to have no damping. In fact, however, various types of energy dissipation mechanisms inevitably lead to the damping even under high vacuum packaging, and for mass sensing scenarios it always operates in high damping environments. The effect of damping on the amplitude and frequency of the weakly-coupled silicon resonator is generally explored by numerical methods. Based on a weak coupling approximation, this article has developed a coupled-mode model for analytically analyzing the effects. A pair of electrostatically-coupled silicon resonator were experimentally fabricated and operated through capacitive transduction. The theoretical and experimental results show a quantitative consistency. The results presented here suggest that it may guide the design of sensors based on mode localization in the presence of damping.