Parametric excitation of circular micromachined polycrystalline silicon disks

Center anchored polycrystalline silicon plates are parametrically excited using ultrasonic substrate motion generated by a lead zirconate titanate oxide (PZT) plate bonded to the silicon die. Parametric excitation is used to achieve large amplitude, greater than 100 nm, transverse plate vibrations in atmospheric pressure with sub-3 VPP drive on the PZT plate with corresponding surface velocities over 1.5 m/s. The preferred 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 Kármán plate equations. Parametric instability is demonstrated with the use of nonlinear Floquet transition matrix.