Micromechanical resonators are promising replacements for quartz crystals for timing and frequency references owing to potential for compactness, integrability with CMOS fabrication processes, low cost, and low power consumption. To be used in high performance reference application, resonators should obtain a high quality factor. The limit of the quality factor achieved by a resonator is set by the material properties, geometry and operating condition. Some recent resonators properly designed for exploiting bulk-acoustic resonance have been demonstrated to operate close to the quantum mechanical limit for the quality factor and frequency product (Q-f). Here, we describe the physics that gives rise to the quantum limit to the Q-f product, explain design strategies for minimizing other dissipation sources, and present new results from several different resonators that approach the limit.

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In this paper, we present four design methods to overcome (100) silicon crystalline anisotropy and achieve modematching in wineglass-mode disk resonator gyroscope (DRG). These methods were validated through experimental characterization of more than 145 different devices that arose from simulations. With the proposed methods, the frequency split of the 250-kHz DRG wineglass modes in (100) silicon was reduced from >10 kHz to as low as 96 Hz (<0.04% of 250-kHz resonant frequency) without any electrostatic tuning. Perfect mode-matching is then achieved using electrostatic tuning. Modematching was maintained within ±10 Hz over a temperature range from −20°C to 80°C. The temperature dependence of quality factor is also discussed in this paper. These results allow for the development of high-performance miniature DRGs tuned for degenerate wineglass mode operation from high-quality crystalline silicon material.[ 2013-0303]Index Terms-Microelectromechanical systems (MEMS) gyroscope, mode-matching, frequency split, (100) single crystal silicon, wineglass mode.

In this paper, we explore the effects of electrostatic parametric amplification on a high quality factor (Q &gt; 100 000) encapsulated disk resonator gyroscope (DRG), fabricated in 〈100〉 silicon. The DRG was operated in the n = 2 degenerate wineglass mode at 235 kHz, and electrostatically tuned so that the frequency split between the two degenerate modes was less than 100 mHz. A parametric pump at twice the resonant frequency is applied to the sense axis of the DRG, resulting in a maximum scale factor of 156.6 μV/(°/s), an 8.8× improvement over the non-amplified performance. When operated with a parametric gain of 5.4, a minimum angle random walk of 0.034°/√h and bias instability of 1.15°/h are achieved, representing an improvement by a factor of 4.3× and 1.5×, respectively.

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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.

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