Thermoelastic Damping In Partially Covered Layered Microbeam And Microplate Resonators

Micromechanical resonators are typical devices of microelectromechanical systems(MEMS),which operate at the resonant frequency excited by an oscillating circuit.Microresonators benefit from the high precision,low latency,large dynamic range.Due to the compatibility with integrated circuit(IC)manufacturing processes,microresonators also has many advantages such as low cost,high integration,and diversified functions.The quality factor(Q–factor)is one of the most critical performance parameters of the microresonators,which directly affects the resolutions and sensitivities.The quality factor is determined by the inherent damping and external damping in the microresonator.The external damping,such as air damping,surface damping and anchor damping,can be eliminated by reasonable design or manufacturing processes.However,intrinsic damping,such as thermoelastic damping(TED),can be reduced and cannot be eliminated,which determines the upper limit of the quality factor of the micromechanical resonator.In recent years,with the rapid development of microresonators,the research of TED has gradually attracted great attention,and has always been one of the research hotspots in the MEMS.With the upgrading of MEMS technology,the traditional monolayer resonators are difficult to meet the increasing requirements for multi–function and high performance.Therefore,complex structural geometries and advanced materials are increasingly applied.In this paper,the TED model of bilayer microbeams,partially covered bilayer microbeams and microplates covered by multicoatings are derived,respectively.The main innovations and results of this dissertation are concluded as follows.First,as for the bilayer microbeam resonators,the two–dimensional(2–D)analytical TED model considering the heat conduction in the thickness and length directions is derived.Two key factors that determine the difference between 2–D model and one–dimensional(1–D)model are summarized.A modified normalized frequency is proposed,the effects of aspect ratio,structural boundary conditions and mode order on TED are analyzed.The results suggest that the accuracy of 2–D model is better than that of 1–D model,but the convergence rate is lower than that of 1–D model.In addition,the multi–peak behaviors of TED frequency spectra are caused by the excessive difference in the thermal diffusivity,rather than the Zener modulus.Secondly,as for the partially covered bilayer microbeam resonators,the 2–D analytical TED model considering the heat conduction in the thickness and length directions is established.The present model can reduce to the 2–D model for the fully covered bilayer beam,and matches well with the finite element method results.The Debye peak behaviors of TED frequency spectra are comprehensively analyzed.The effects of the length and position of the metal coating on the TED at the fundamental mode are evaluated.The results show that the convergence rate of present model is lower than that of the monolayer model,but higher than that of the fully covered bilayer beam model.To reduce TED,the metal coating should be arranged far away from the clamping end of the beam.Specifically,for cantilever beams,the coating should be placed on the free end instead of the clamped end.The length ratio of the coating layer to the substrate layer should not exceed 0.6.For doule clamped beams,when the length ratio exceeds 0.7,TED values increase significantly.The research of this dissertation provides some new perspectives for controlling TED.Finally,as for the circular microplate resonators partillay covered by multiple coatings,a theoretical framework for TED is developed.Meanwhile,a simple model for rapid evaluation of TED is proposed.The convergence rates of present model are analyzed,and the accuracy and application of the simple model are studied.The effects of the radius,thickness and position of the coating on the TED at the fundamental mode are evaluated.The analysis of this dissertation found that the convergence rate of present model decreases with the increase of the coating thickness and covered region.At the same time,the Si O₂ coating can suppress the TED,and the reduction of TED increases as the thickness and coverage of the Si O₂ coating increase.To minimize the TED,Si O₂ coating should fully cover the Si layer.In addition,the imperfect thermal contact interface increases the TED values,and effects of coating radius and thickness on TED cannot be ignored with the low contact thermal conductivity.