Multiplication in Frequencies by Synchronized and Superharmonic Oscillations: Sensing Verification With Picogram Order Microspheres

The frequency multiplication in a simplified two-cantilever system was characterized and its mass sensing capability was demonstrated. Two microcantilevers similar in cross section but different in length, with primary frequencies of 177.38 kHz [ω1 of (long) low-frequency cantilever] and 351.66 kHz [ω₂ of (short) high-frequency cantilever], are connected micromechanically with each other by a coupling overhang. In synchronized regime, when the long cantilever is excited at its primary frequency of ω₁, the frequency response of the coupled short cantilever has a peak at double the primary frequency of 2 ω₁ of the long cantilever. While in superharmonic oscillation, the drive frequency of 0.5 ω₂ was multiplied to ω₂ with a higher vibration power along high-frequency cantilever. Mass sensing in picogram order was demonstrated by applying polystyrene microspheres as a small mass perturbation onto the tip of low-frequency cantilever. Comparing with no mass perturbation, almost no frequency shift was observed in superharmonic oscillation although the vibration power decreased slightly, while the frequency shift was multiplied by a factor of n = 2 from 6.13 to 12.26 kHz with a slightly increased vibration power due to synchronized oscillation. A mass of 8.609 pg was then derived for the applied polystyrene microspheres, corresponding to the calculated value of 8.792 pg from geometrical size and chemical density. To the best of our knowledge, this is the first experimental demonstration of synchronized oscillation used for picogram mass sensing, as well as the original comparative study of the frequency multiplication conducted by synchronized oscillation with respect to superharmonic one.