Electrical characterization of thin-film silicon flexural resonators in linear and nonlinear regimes of motion for integration with electronics

The integration of microelectromechanical devices (MEMS) with its driving integrated circuits is fundamental to expanding the applications of both technologies. This integration puts important demands on the MEMS processing and their electromechanical performance. This work presents the electrical characterization of flexural microresonators made of hydrogenated amorphous silicon fabricated on glass substrates at temperatures compatible with CMOS backend processing (175 °C). Submicron transduction gaps with thicknesses ranging from 250 nm to 600 nm are demonstrated. The resonators are electrostatically actuated and their motion is capacitively sensed. The resonant motion of the flexural resonator in the linear regime is modeled by an equivalent electrical circuit, comprising a series RLC with a parallel capacitor. The motional resistance, Rm, of the system is studied as a function of the transduction gap thickness and the dc voltage applied to the resonator and a minimum value of ∼85 kΩ is measured. A hysteresis criterion based on geometric and material properties of the resonators is applied to the experimental results of a resonator that shows mechanical stiffening, allowing the prediction of the onset of hysteresis and the development of a design rule to minimize the motional resistance. The electrical model loses its validity when the resonators enter a nonlinear regime of motion, which is shown to occur either by mechanical stiffening or electrical softening. Strategies to extract the linear, k1m, and cubic, k3m, mechanical coefficients of the spring constant are presented and applied to the experimental results.