Parametric excitation of whispering gallery modes on circular micromachined polysilicon disks

Center anchored polysilicon plates are parametrically excited with ultrasonic substrate motion. The substrate motion is generated by a PZT plate bonded to the silicon die. Parametric excitation is used to achieve large amplitude, over 100 nm, transverse plate vibrations in atmospheric pressure with sub-3 V_PP drive on the PZT plate. The parametrically excited modes are observed to be "whispering gallery" plate modes with no radial nodal points. The possible nonlinear mechanisms are analyzed and the parametric excitation is explained with in-plane plate stresses due to the lateral plate anchor motion. The effect of in-plane stresses is modeled with von Karman plate equations. Parametric instability is demonstrated with the use of the Floquet transition matrix.