We present the development of millimeter scale 3D hemispherical shell resonators fabricated from the polycrystalline diamond, a material with low thermoelastic damping and very high stiffness. These hemispherical wineglass resonators with 1.1 mm diameter are fabricated through a combination of micro-electro discharge machining (EDM) and silicon micromachining techniques. Using piezoelectric and electrostatic excitation and optical vibration measurement, the elliptical wineglass vibration mode is determined to be at 18.321 kHz, with the two degenerate wineglass modes having a relative frequency mismatch of 0.03%. A study on the effect of the size and misalignment of the anchor and resonator's radius variation on both the average frequency and frequency mismatch of the 2θ elliptical vibration modes is carried out. It is shown that the absolute frequency of a wineglass resonator will increase with the anchor size. It is also demonstrated that the fourth harmonic of radius variation is linearly related to the frequency mismatch.

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We present a demonstration of a whole-angle mode operation of a 0.6 mm single-crystal silicon disk resonator gyroscope (DRG). This device has a Q factor of ~80,000 and a resonant frequency of ~250 kHz and is fabricated in the epi-seal process. Discrete-time control algorithms for rate-integrating gyro operation were implemented based on Lynch's algorithm. Despite the fact that this DRG is over 5 orders of magnitude smaller than the 58 mm HRG, the device's error sources are shown to be accurately modeled by the basic error models developed by Lynch.

Resonators used in frequency-reference oscillators must maintain a stable frequency output even when subjected to temperature variations. The traditional solution is to construct the resonator from a material with a low temperature coefficient, such as AT-cut quartz, which can achieve absolute frequency stability on the order of ±25 ppm over commercial temperature ranges. In comparison, Si microresonators suffer from the disadvantage that silicon's temperature coefficient of frequency (TCF) is approximately two orders of magnitude greater than that of AT-cut quartz. In this paper, we present an in situ passive temperature compensation scheme for Si microresonators based on nonlinear amplitude-frequency coupling which reduces the TCF to a level comparable with that of an AT-quartz resonator. The implementation of this passive technique is generic to a variety of Si microresonators and can be applied to a number of frequency control and timing applications.

We demonstrate synchronization between two intrinsically coupled oscillators that are created from two distinct vibration modes of a single micromachined disk resonator. The modes have a 3:1 subharmonic frequency relationship and cubic, non-dissipative electromechanical coupling between the modes enables their two frequencies to synchronize. Our experimental implementation allows the frequency of the lower frequency oscillator to be independently controlled from that of the higher frequency oscillator, enabling study of the synchronization dynamics. We find close quantitative agreement between the experimental behavior and an analytical coupled-oscillator model as a function of the energy in the two oscillators. We demonstrate that the synchronization range increases when the lower frequency oscillator is strongly driven and when the higher frequency oscillator is weakly driven. This result suggests that synchronization can be applied to the frequency-selective detection of weak signals and other mechanical signal processing functions.

The hemispherical resonator gyro (HRG) is low loss and high stability, spurring recent interest in micro-scale hemispherical resonators. To achieve mode-matching and high-Q performance in a hemispherical resonator, geometric symmetry in combination with low thermoelastic damping structural material are critical. In this work, we describe the development of millimeter scale 3D hemispherical shell resonators fabricated from polycrystalline diamond, a material with low thermoelastic damping and very high stiffness. The relation between the fourth harmonic (4θ) in a Fourier analysis of the resonator's radius r(θ) and frequency mismatch (Δf) of the 2θ elliptical vibration modes of the shell resonator is demonstrated.

In this letter, we investigate the dynamics of injection-locking a nonlinear micromechanical oscillator operating in different regimes of electromechanical nonlinearity to an external tone generated by a secondary oscillator. The micromechanical oscillator exhibits a combination of mechanical and electrostatic nonlinearities that were tuned using a bias voltage to adjust the relative importance of third-order and fifth-order stiffness nonlinearities. While it is well-known that third-order stiffness (Duffing) nonlinearity results in a synchronization range that increases with an oscillator's amplitude, little is known about the impact of other nonlinearities. We show that when using Duffing nonlinearity cancellation, higher order nonlinearities dominate, the synchronization range is smaller but has a greater rate-of-increase with oscillation amplitude. When both mechanical stiffness-hardening and electrostatic stiffness-softening nonlinearities are present, the frequency response follows an “s-curve” and, unlike the other conditions, the synchronization range does not increase monotonically with amplitude but instead reaches a minimum when both nonlinearities have similar magnitude. We develop a nonlinear resonator model and show that this model achieves good quantitative prediction of the measured synchronization range in all nonlinear operating regimes studied.

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