Geometric effects on thermoelastic damping in MEMS resonators

• Published in: Journal of sound and vibration Vol. 309; no. 3; pp. 588 - 599
• Main Author: Yi, Y.B.
• Format: Journal Article
• Language: English
• Published: London Elsevier Ltd 22.01.2008; Elsevier
• Subjects: Exact sciences and technology; Fundamental areas of phenomenology (including applications); Instruments, apparatus, components and techniques common to several branches of physics and astronomy; Mechanical instruments, equipment and techniques; Micromechanical devices and systems; Physics; Solid mechanics; Structural and continuum mechanics; Energy function; Fourier analysis; Simple support; Axial symmetry; Finite element method; Loss function; Vibration damping; Energy dissipation; Quality factor; Resonance frequency; Perturbation techniques; Rings; Size effect; Energy losses; Thermoelasticity; Modelling; Eigenvalue problem; Silicon; Resonators; Microelectromechanical device
• ISSN: 0022-460X; 1095-8568
• DOI: 10.1016/j.jsv.2007.07.055

The effects of geometry on the energy dissipation induced by thermoelastic damping in MEMS resonators are investigated numerically using a finite element formulation. The perturbation analysis is applied to derive a linear eigenvalue equation for the exponentially decaying rate of the mechanical oscillation. The analysis also involves a Fourier method that reduces the dimensionality of the problem and considerably improves the computational efficiency. The method is first validated by comparing the two-dimensional model to the existing analytical solutions for a simply supported beam system, and then it is extended to a three-dimensional axisymmetric geometry to obtain the energy loss as a function of the geometric parameters in a silicon ring resonator. The computational results reveal that there is a peak value for the resonant frequency when the radial width of the ring varies. In addition, the quality factor ( Q-factor) decreases with the radial width as a monotonic function.