Acceleration sensitivity of small-gap capacitive micromechanical resonator oscillators

Abstract

Abstract-The vector components of acceleration sensitivity Γ for a closed-loop oscillator referenced to a wine-glass disk arraycomposite resonator employing tiny (~92nm) electrode-toresonator capacitive transducer gaps were measured along axes perpendicular and parallel to the substrate to be Γ vertical~1 3.6ppb/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 boardlevel realization of the oscillator, so are very likely not representative of the performance actually achievable by a fullyintegrated 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-toresonator 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.

A low phase-noise Pierce oscillator using a piezoelectric-on-silica micromechanical resonator

“…This result is comparable with some SC-cut quartz-based oscillators. However, we believe that the vibration sensitivity is still dominated by the electrical components in the measurement setup [11], including bondwires, electrical connections, etc. The silica resonator itself should have significantly smaller vibration sensitivity.…”

A negative-capacitance equivalent circuit model for parallel-plate capacitive-gap-transduced micromechanical resonators

“…although solution of (22)-(24) as described provides an accurate value for the resonance frequency of the wineglass [i.e., compound-(2, 1)] mode, it does not readily impart design insight. To provide better insight to variable dependencies, rearrangement and simplification of (22)- (24) yields the closed form…”

“…Interestingly, the most significant mechanism for frequency instability caused by these particular perturbations ends up being instability in the electrical stiffness. For instance, theoretical analysis of micromechanical wine-glass disk resonators reveals that acceleration-induced changes in electrode-to-resonator gap spacing or overlap area that in turn induce shifts in electrical stiffness dominate among sources that shift frequency during accelerations [24]. In addition, noise or drift on the power supply manifests as fluctuations on the resonator dc-bias V P that obviously destabilize the electrical stiffness, and thereby, resonance frequency.…”

“…-(24) for ζ = ζ (n,m),mat then substituting this value into(26). For polysilicon structural material (with E = 150 GPa, ρ = 2300 kg/m 3 , and σ = 0.226), ζ (2,1),polysi = 2.344, and K (2,1),polysi = 0.476.…”

Micromechanical disk array for enhanced frequency stability against bias voltage fluctuations

“…As the electrical stiffness of a capacitive-gap MEMS resonator is often determined by dc-bias voltage , electrode-to-resonator overlap capacitance , and the capacitive gap spacings , environmental fluctuations that disturb any of these parameters will cause instability in electrical stiffness and generate frequency shift, as shown in Figure 1.2. For instance, theoretical analysis of micromechanical wine-glass disk resonators reveals that acceleration-induced changes in electrode-to-resonator gap spacing or overlap area that in turn induce shifts in electrical stiffness dominate among sources that shift frequency during accelerations [7]. In addition, noise or drift on the power supply manifests as fluctuations on the resonator dc-bias VP that obviously destabilize the electrical stiffness, and thereby, resonance frequency [4].…”