Geometric effects on thermoelastic damping in MEMS resonators

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.