Simple measurement technique for resonance frequency of micromachined cantilevers

This paper discusses a simple electrical measurement technique to determine resonance frequency of surface micromachined cantilever beams that is also suitable for packaged devices. Measurements are done on oxide anchored doped polysilicon beams. If the beam is driven by an AC signal riding on the DC bias, the beam starts vibrating. When the drive frequency matches the natural frequency of the beam, the oscillation amplitude is maximum. In this measurement, the DC bias is fixed at a value lower than the pull-in voltage. A small AC bias is then applied such that the sum of the DC and the maximum amplitude of the AC is less than the pull-in voltage. The frequency of the AC is then swept and at resonance, because of large displacement, the beam is pulled in and this is detected by a current flowing between the beam and the substrate. By iteratively adjusting the DC bias it is possible to make sure that pull-in occurs only due to resonance and the frequency setting at this point gives the natural frequency of the beam. Measured values for different beam lengths were compared with Doppler Vibrometry results and gave an excellent match.