Inclination Effects on Voltage-controlled Tuning of MEMS Disk Resonator Array Composite Fabricated by Deep Reactive Ion Etching Process

Abstract

Capacitive micro-electromechanical system (MEMS) disk resonators fabricated by deep reactive-ion etching (DRIE) have large sensitive capacitances and low motional resistances. However, for the MEMS disk structure with a high aspect ratio, the cross section takes on a trapezoidal profile, which will affect the performance of the resonator. In this study, we firstly analyzed the electrostatic tuning mechanism of electrical stiffness produced by the electrostatic force, and the dependence of resonance frequency variation on the inclination angle and dc bias voltage is obtained and the electromechanical coupling strength was changed owing to the inclination angle. Secondly, after analyzing the feasibility of overcoming the inclination effect by introducing a tuning disk array, the optimal tuning voltage of the inclined disk resonator array and the scale of the array with a small motional resistance can be obtained. The results show that, for an array with the same inclination angle of 0.1° and biased at 10 V, when the tuning voltage is 20 V, the relative error of the resonance frequency can be reduced to 12.4 ppm. In addition, the optimal tuning voltage increases as the inclination angle increases, and when the inclination angle is 0.3°, the optimal tuning voltages are 28.68 and 57.35 V for the dc bias voltages of 10 and 30 V, respectively. If the motional resistance needs be reduced to 50 Ω, the integrated number of disk resonators will increase to 1048, and the optimal tuning voltage can reach 37.5 V. These results can provide some theoretical basis for the large-scale integration of the disk resonator array in the future.

Inclination Effect on the Periodic Response of a Symmetrical MEMS Gyroscope

“…Zhong et al [ 13 ] studied the inclination effect of the fingers on the capacitance, driving electrostatic force, and electrostatic spring constant and discussed the nonlinear dynamics of a MEMS resonator. Yan et al [ 14 ] analyzed the electrostatic tuning mechanism of electrical stiffness produced by the electrostatic force and gave the dependence of resonance frequency variation on the inclination angle and DC bias voltage of an inclined disk resonator array. Zhang et al [ 15 ] studied the influence of inclination angle on the resonance frequency, stiffness hardening effect, and sensitivity of a 4-DOF MEMS gyroscope.…”