Thermoelastic Damping Of Single Crystal Silicon Thin Plate Microresonator

Micromechanical resonators are one of the MEMS devices that operate mainly at resonant frequencies.Quality factor is an important parameter to measure the performance of micromechanical resonators.Thermoelastic damping is an important energy dissipation mechanism for high quality factor micromechanical resonators and belongs to the internal damping of materials.In order to fabricate high quality factor microresonators,it is necessary to study the generation mechanism of thermoelastic damping.Single crystal silicon is a common material for the manufacture of micromechanical resonators.Previously,the research objects of thermoelastic damping of micromechanical resonators were mainly microbeams,microrings and microplates based on isotropic materials.Based on the theory of anisotropy,this paper studies the one-dimensional thermoelastic damping analytical model of single crystal silicon rectangular thin plate microresonator,the three-dimensional thermoelastic damping analytical model of single crystal silicon rectangular thin plate microresonator and the single crystal silicon circular thin plate microresonator.One-dimensional thermoelastic damping analytical model.The main innovations and research results of this paper are as follows:Firstly,taking the single crystal silicon rectangular thin plate as the research object,the one-dimensional temperature field function is solved by the separation variable method,and then the one-dimensional thermoelastic damping analytical model is given.The thermoelastic damping results of isotropic single crystal silicon are compared with those of anisotropic single crystal silicon,and the effects of length-to-thickness ratio,rotation angle and two typical thinplate mode functions on thermoelastic damping are studied.It is found that the thermoelastic damping analytical model of anisotropic single crystal silicon has a better fit with the finite element model.When the aspect ratio is greater than 20,the fitting degree of this model is higher.When the rotation angle increases from 0° to 45°,the thermoelastic damping results of the single crystal silicon rectangular sheet gradually decrease,and the influence of the mode shape function on the analytical model can be ignored.Secondly,still taking the single crystal silicon rectangular sheet as the research object,on the basis of the one-dimensional thermoelastic damping model,the three-dimensional temperature field function is obtained by the thermal mode superposition method,and the threedimensional thermoelastic damping analytical model is established.In this paper,the fitting degree of one-dimensional and three-dimensional thermoelastic damping analytical models and finite element models are compared,and the effects of rotation angle and aspect ratio on thermoelastic damping are discussed.The study found that when the aspect ratio was between10 and 40,the three-dimensional model fit better than the one-dimensional model.And when the rotation angle is 45°,the thermoelastic damping value of the micro-resonator device is the smallest.Finally,taking the single crystal silicon circular thin plate as the research object,a onedimensional thermoelastic damping analytical model of the single crystal silicon circular thin plate microresonator is derived.The effects of diameter-to-thickness ratio and rotation angle on the thermoelastic damping value were studied.It is found that the thermoelastic damping value of the single crystal silicon disc is independent of the rotation angle.When the ratio of diameter to thickness is greater than 15,the maximum value of the thermoelastic damping of the microcircular plate has the highest fitting degree with the analytical model when the rotation angle is20°.