Parametric excitation of flexural vibrations of micro beams by fringing electrostatic fields

We report on an approach for efficient excitation of large amplitude flexural out-of-plane vibrations of micro beams and present results of theoretical and experimental feasibility study of the suggested principle. An actuating electrode is located symmetrically at the two sides of the beam and is fabricated from the same layer of the wafer. The electrostatic force is engendered by the asymmetry of the fringing fields in the deformed state and acts in the direction opposite to the deflection therefore increasing the effective stiffness of the system. The time-varying voltage applied to the electrode results in the modulation of this electrostatic stiffness and consequently in the parametric excitation of the structure. The device may exhibit large vibrational amplitudes not limited by the pull-in instability common in close-gap actuators. In contrast to previously reported devices excited by the fringing fields, the force considered here is of distributed character. The reduced order model was built using the Galerkin decomposition with linear modes as base functions and the resulting system of nonlinear differential equations was solved numerically. The electrostatic forces were approximated by means of fitting the results of three-dimensional numerical solution for the electric fields. The devices fabricated from a silicon on insulator (SOI) substrate using deep reactive ion etching (DRIE) based process were operated in ambient air conditions and the responses were registered by means of Laser Doppler Vibrometry. The experimental resonant curves were consistent with those predicted by the model. Theoretical and preliminary experimental results illustrated the feasibility of the suggested approach.