Microelectromechanical Resonator Characterization Using Noncontact Parametric Electrostatic Excitation and Probing

A noncontact electrostatic probing technique using a scanning probe microscopy cantilever is shown to actuate and detect the resonant behavior of a micromachined resonator. The method is capable of characterizing a resonator with resonant frequency much greater than that of the cantilever. The coupled oscillator model developed for this system describes the resonant response of the test resonator as detected through the probe, including the fourth-power dependence on the probe drive voltage. The veracity of this model is demonstrated through comparison with experimental data obtained from a test resonator with a resonant frequency ten times greater than the resonant frequency of the probe cantilever. This technique yields a straightforward determination of the resonant frequency and quality factor of a micromachined resonator, avoiding limitations due to optical interference and any reliance on a supporting circuitry.