A dual mass vibratory gyroscope sensor demonstrates the quadrature frequency modulated (QFM) operating mode, where the frequency of the circular orbit of a proof mass is measured to detect angular rate. In comparison to the mode-matched open loop rate mode, the QFM mode receives the same benefit of improved SNR but without the penalties of unreliable scale factor and decreased bandwidth. A matched pair of gyroscopes, integrated onto the same die, is used for temperature compensation, resulting in 6 ppb relative frequency tracking error, or an Allan deviation of 370 deg/hr with a 70 kHz resonant frequency. The integrated CMOS electronics achieve a capacitance resolution of 0.1 zF/rt-Hz with nominal 6 fF sense electrodes.

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.

Thin-film microcrystalline diamond micromechanical resonators with mechanical quality factor limited by thermoelastic dissipation in the diamond film are demonstrated. Surface micromachined double ended tuning fork resonators were fabricated from in-situ boron doped microcrystalline diamond films deposited using hot filament chemical vapor deposition. Time-domain thermoreflectance measurements show thermal conductivity of 110 W m À1 K À1 for heat transport through the thickness of the diamond film. Measurement of the quality factor of resonators spanning a frequency range 0.5-10 MHz shows a maximum Q ¼ 81 646 and demonstrates good agreement with quality factor limited by thermoelastic dissipation using 100 W m À1 K À1 for the in-plane thermal conductivity of the diamond film. V

We demonstrate high quality factor thin-film nanocrystalline diamond micromechanical resonators with quality factors limited by thermoelastic damping. Cantilevers, single-anchored and double-anchored double-ended tuning forks, were fabricated from 2.5 μm thick in-situ boron doped nanocrystalline diamond films deposited using hot filament chemical vapor deposition. Thermal conductivity measured by time-domain thermoreflectance resulted in 24 ± 3 W m−1 K−1 for heat transport through the thickness of the diamond film. The resonant frequencies of the fabricated resonators were 46 kHz–8 MHz and showed a maximum measured Q ≈ 86 000 at fn = 46.849 kHz. The measured Q-factors are shown to be in good agreement with the limit imposed by thermoelastic dissipation calculated using the measured thermal conductivity. The mechanical properties extracted from resonant frequency measurements indicate a Young's elastic modulus of ≈788 GPa, close to that of microcrystalline diamond.

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.