A triangular electrostatic comb array for micromechanical resonant frequency tuning

A new electrostatic comb structure has been presented for the post-fabrication frequency tuning of laterally driven micromechanical resonators. The frequency tuning comb structure, composed of a triangular comb array of linearly varied finger lengths, generates a linear electrostatic tuning force from the translational motion of the DC-biased comb array. Simple analytic formulae for the electrostatic tuning force, the modified stiffness, and the resonant frequency have been derived in terms of the tuning bias voltage. A set of frequency tunable microresonators has been designed and fabricated by the 4-mask surface-micromachining process. The resonant frequency of the microfabricated microresonator has been measured as 2.42 kHz at the reduced pressure of 1 Torr. The resonant frequency has been reduced by 3.3% for a tuning voltage increase of 20 V. The theoretical frequency shift, including the electrostatic levitation effect, is compared with the experimental results. The higher tuning voltage results in the lower effective stiffness, thereby decreasing resonant frequency of the microresonator. (C) 1998 Elsevier Science S.A. All rights reserved.