Thermoelastic damping and support loss in MEMS ring resonators

Micro Electro-Mechanical Systems (MEMS) rate sensors are inertial devices based on a resonating structure to measure and detect rate of angular rotation. For applications requiring high performance angular rate measurements it is important to be able to design MEMS rate sensors with high quality factors (Q-factor or Q). However, the device performance is affected by physical damping mechanisms which influence the overall quality factor of the device. High performances from a damping perspective can be achieved by identifying the dominant damping mechanism and considering different ways to reduce damping. For vacuum encapsulated devices, thermoelastic damping (TED) and support loss are the most important damping mechanism in MEMS resonators. This thesis focuses on understanding and quantifying the effects of thermoelastic damping and support loss on the damping performance of a supported ring resonator. An extensive review of different methods of modelling TED and support loss is presented. It is concluded that analytical models are not applicable to complex structures to predict damping due to their restrictive assumptions, and numerical approaches are required for accurate prediction. In this thesis a finite element based model using a fully coupled thermo-elastic approach is developed to quantify the thermoelastic dissipation in supported ring resonators and a detailed parameter study is conducted to understand the influence of ring geometry, support legs, micro-machined slots around the ring circumference, and material properties. The results show that damping in the support legs can have significant influence on TED in the resonator, and the optimum leg geometry can be identified to achieve high-Q. It is also observed that the addition of slots improves Q for resonators having higher energy loss. However, for high-Q rings slots have a detrimental effect. The results are considered for designing high-Q ring resonators with reduced levels of thermoelastic damping, and devices fabricated based on high TED Q designs are tested experimentally to compare the performance with predicted values. To analyse support loss behaviour in supported rings, a finite element model is developed using Perfectly Matched Layer (PML) technique to accurately predict the dissipation of energy through the elastic wave propagation from the resonator into its substrate. The model is validated by identifying key modelling issues, and strategies have been developed to effectively calculate PML parameters are discussed. The model is used to analyse support loss in supported ring resonators, and it is concluded that support loss is negligible compared to TED. Further investigations consider the effect of key design parameters on support loss, including a quantitative evaluation of the influence of an unbalanced vibration on the support loss by considering systematic design variation and manufacturing imperfections in the supported ring resonators. It is concluded that mass imperfection in the resonator and cycling asymmetry of the central supporting structure not only induce frequency splitting between degenerate pair of modes but also increase support loss due to the unbalance of the mode. It is expected that the results and contributions of this work will aid the development of high performance MEMS angular rate sensors by reducing the damping behaviour