Generic Temperature Compensation Scheme for CMOS-MEMS Resonators Based on ARC-Beam Derived Electrical Stiffness Frequency Pulling

This work demonstrates a generic temperature compensation scheme applicable for nearly all types of resonators in CMOS-MEMS technology without additional process steps. Particularly, based on the arc-beam structure used for gap narrowing, specific geometrical design yields autonomous temperature dependent gap spacing between the tuning electrode and the resonator body and in turn results in electrical stiffness necessary for counteracting resonance frequency variation at varying temperatures. Using a clamped-clamped beam (CC-beam) resonator in the 0.35-µm CMOS-MEMS process platform as a demonstration vehicle, the compensation scheme reduces the first-order temperature coefficient (TCF
1
) from -394.16 ppm/°C to +14.18 ppm/°C with a TCF
2
of -1.5757 ppm/°C
²
from 0 °C to 90 °C. With the help of the gap variation prediction model derived and knowledge of stress information, the arc-beam structure offers an elegant solution of temperature compensation for CMOS-MEMS resonators with inherent yet thermally induced stress.