Micromechanical disk array for enhanced frequency stability against bias voltage fluctuations

A 215-MHz polysilicon capacitive-gap transduced micromechanical resonator array employing 50 mechanically coupled radial-contour mode disks - the largest such array yet fabricated and measured - has achieved 3.5× better frequency stability than single stand-alone disks against fluctuations in the dc bias voltage (V_P) normally applied across electrode-to-resonator gaps during device operation. The key to enhanced frequency stability is the electrode-to-resonator capacitance (C_o) generated by the parallel combination of input/output electrodes overlapping each resonator in the array that in turn reduces the efficacy of the bias voltage-controlled electrical stiffness. Here, a new equivalent circuit based on negative capacitance provides improved visualization that helps to identify methods to suppress electrical stiffness induced frequency variation. The circuit model indicates that the more resonators in an array, the smaller the frequency shift imposed by a given bias voltage change. Both modeling and measurement suggest that the most stable MEMS-based oscillators (e.g., against supply noise and acceleration) are ones that utilize mechanically-coupled arrays of resonators.