Design of a Multiple Folded-Beam Disk Resonator with High Quality Factor.

This paper proposes a new multiple folded-beam disk resonator whose thermoelastic quality factor is significantly improved by appropriately reducing the beam width and introducing integral-designed lumped masses. The quality factor of the fabricated resonator with (100) single crystal silicon reaches 710 k, proving to be a record in silicon disk resonators. Meanwhile, a small initial frequency split of the order-3 working modes endows the resonator with great potential for microelectromechanical systems (MEMS) gyroscopes application. Moreover, the experimental quality factor of resonators with different beam widths and relevant temperature experiment indicate that the dominating damping mechanism of the multiple folded-beam disk resonator is no longer thermoelastic damping.

Shape, Resonant Frequency and Thermoelastic Dissipation Analysis of Free-Formed Microhemispherical Shells Based on Forming Process Modeling.

Free-form microhemispherical shell resonators have the advantages of high quality factor and mass production. The shape of microhemispherical shells created via this process is based on a single mold and is difficult to adjust, which affects the resonant frequency and quality factor. In this paper, a process analysis model is established through in-depth analysis of the process mechanism and flow of the free-forming method. Based on this model, the influence of the designed preforming parameters on the shape, resonant frequency and thermoelastic dissipation of the microhemispherical shell are analyzed in detail, providing theoretical guidance for parameter design. The results show that the depth and the ratio of internal to external pressure of the substrate's annular groove affect the height and thickness of the microhemispherical shell, and the structural thickness affects the thickness of the microhemispherical shell; these in turn affect the resonant frequency and thermoelastic dissipation of the microhemispherical shell resonator. In addition, the inner diameter of the substrate's annular groove mainly affects the radius of the support column of the microhemispherical shell, and the influence on the resonant frequency and thermoelastic dissipation of the resonator is relatively low.

A 5.86 Million Quality Factor Cylindrical Resonator with Improved Structural Design Based on Thermoelastic Dissipation Analysis.

The cylindrical resonator is the core component of cylindrical resonator gyroscopes (CRGs). The quality factor (Q factor) of the resonator is one crucial parameter that determines the performance of the gyroscope. In this paper, the finite element method is used to theoretically investigate the influence of the thermoelastic dissipation (TED) of the cylindrical resonator. The improved structure of a fused silica cylindrical resonator is then demonstrated. Compared with the traditional structure, the thermoelastic Q (QTED) of the resonator is increased by 122%. In addition, the Q factor of the improved cylindrical resonator is measured, and results illustrate that, after annealing and chemical etching, the Q factor of the resonator is significantly higher than that of the cylindrical resonators reported previously. The Q factor of the cylindrical resonator in this paper reaches 5.86 million, which is the highest value for a cylindrical resonator to date.

Investigation on the Quality Factor Limit of the (111) Silicon Based Disk Resonator.

Quality factor is one of the most important parameters for a MEMS resonator. Most MEMS resonators are dominated by thermoelastic dissipation (TED). This paper demonstrates that the TED in a disk resonator that is made of (111) single-crystal silicon is surpassed by clamping loss. The stiffness-mass decoupling design method, combined with reducing the beam width, was used to engineer high QTED. Experiments show that Q of the (111) disk resonator have an upper boundary that is determined by the clamping loss caused by the unbalanced out-of-plane displacement. The origin of the out-of-plane displacement is explained by theory and simulation.