M.Sc Thesis | |

M.Sc Student | Levi Sivan |
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Subject | Wineglass Mode Resonators with Optimized Geometry for Mode Matching and Mode Ordering |

Department | Department of Mechanical Engineering |

Supervisor | PROF. David Elata |

Full Thesis text |

Resonators are an essential building block in sensors, oscillators and filters. Traditionally, microscale resonators have been implemented in electronic circuits, but recently MEMS resonators are becoming increasingly prevalent, due to their higher quality-factor and superior performance. MEMS resonators are used in many applications, mainly as sensors, filters and oscillators. One class of MEMS resonators utilize the wineglass modes of disc or annular structures for the intended application.

In this research we study various types of bulk-mode resonators, in which a single deformable structure provides both inertia and stiffness. MEMS resonators are most often fabricated from (100) single crystalline silicon (SCS), which is an anisotropic material. Due to this anisotropy, modes which occur at the same frequency in isotropic materials, occur at different frequencies, resulting in mode mismatch. The mode mismatch in the n=2 wineglass modes of disc resonators is shown in finite elements simulations and demonstrated in experiment. We then present two possible design strategies which achieve mode matching in resonators operating at the n=2 wineglass mode. Simulations of the proposed resonators are presented, and experimental validation is performed for one of the suggested designs.

Following this, we discuss the mode ordering phenomenon, where the relative frequencies of different structural modes is manipulated. Specifically, we are interested in making the n=0 wineglass mode the lowest frequency mode. We suggest a resonator geometry aimed at achieving the n=0 wineglass mode ordering and validate this with finite elements simulations.

The work on mode ordering turned our attention to the static solid mechanics problem of the guided-guided beam. We present a mathematical model for this problem, along with an analytical solution and a finite elements model and solution. Additionally, an experimental model demonstrating the validity of the theoretical predictions is presented.

The overall objective of the work presented here is to optimize the performance of MEMS wineglass mode resonators. Two specific directions of achieving this optimization are considered. The first direction is seeking a possible structure of an annular ring in which the axisymmetric (i.e., the 0th order wineglass mode), is the mode with the lowest eigenfrequency. Since this is impossible to achieve in an annular ring that is made from isotropic elastic material, we will consider an annular ring that is made from spokes and flexures. The second direction is seeking new ways to overcome frequency mismatch between the two conjugate 2nd order wineglass modes in a disk that is made from anisotropic single-crystalline silicon. In isotropic elastic disks, the two conjugate 2nd order wineglass modes are degenerate, and they have a similar mode-shape and frequency. To achieve this, we use piezoelectric thin film actuation in MEMS to drive and sense resonating structures. We demonstrate mode matching of the 2nd order wineglass in disk-like bulk resonators by structural shape optimization. Specifically, we propose a flower-shaped resonator and a button-shaped resonator, in which the two conjugate 2nd order modes have the same natural frequency, even though they are made from anisotropic silicon.