Acceleration sensitivity of small-gap capacitive micromechanical resonator oscillators

The vector components of acceleration sensitivity Γ for a closed-loop oscillator referenced to a wine-glass disk array-composite resonator employing tiny (~92 nm) electrode-to-resonator capacitive transducer gaps were measured along axes perpendicular and parallel to the substrate to be Γ_vertical~13.6ppb/g and Γ_lateral~4.92ppb/g, respectively, which are on par with commercial quartz-based oscillator products. Interestingly, the measured acceleration sensitivity greatly exceeds the prediction of theory. In particular, models for frequency shifts due to variations in electrical stiffness and mechanical stress predict acceleration sensitivities orders of magnitude lower than measured here. Consideration of other microphonic contributors reveals that the measurements of this work were probably limited by the bond wires and package stresses of the board-level realization of the oscillator, so are very likely not representative of the performance actually achievable by a fully-integrated micromechanical resonator oscillator, where MEMS and transistors share a single chip. Still, the measured microphonic performance on par with mid-grade quartz oscillators at least provides some reassurance that the tiny electrode-to-resonator gaps used in high frequency capacitively transduced micromechanical resonators will not compromise the stabilities of oscillators referenced to them in conventional applications that currently accept mid-grade quartz resonators.