Thermoelastic damping analysis of double clamped microbeams with exponentially tapered thickness

For microbeam resonators operated in vacuum, thermoelastic damping (TED) has been theoretically and experimentally verified as a fundamental mechanism of energy loss. Especially, the upper limitation of quality factor of resonators is determined by thermoelastic damping. There are two classical models developed by Zener and Lifshits and Roukes (LR) for evaluating TED. However, the classical models are imprecise to calculate TED values of non-uniform microbeams. In this study, a modified TED model for non-uniform microbeams with exponentially tapered thickness is proposed basing on Zener's theory. The constraint boundary condition of doubly clamped usually encountered in MEMS field is taken into account. The modal parameters of non-uniform beams considered in this work are solved by the modified Adomian decomposition method. Results show that TED values of the present model agree well with those of the finite element method (FEM) model. At low frequencies, TED values of exponentially tapered microbeams are lower than those of uniform microbeams. Additionally, the value of Debye peak of exponentially tapered microbeams is approximately 0.474Δ_E that is lower than 0.5Δ_E of the uniform microbeam.

I. Introduction

In real applications, micro-electro-mechanical systems (MEMS) beam resonators are popular devices used in many fields, such as frequency filters, pressure sensors, accelerometers, and inertial sensors [1]–[3]. Due to the improving manufacture technologies of MEMS, non-uniform micro beam resonators with varying cross-section have been considered seriously for their enhanced properties, such as stepped microbeam, slotted microbeam, torsion microbeam and tapered microbeam. As a significant parameter evaluating the resonator performance, quality factor is crucial to design non-uniform micro resonators. Achieving higher value of quality factor is a important and significant task for designers. According to the experimental results, the upper limitation of quality factor in microresonators operated in vacuum is dominated by thermoelastic damping (TED). Unfortunately, eliminating the TED effect completely is impossible. Thereby for the optimization of non-uniform microresonators, estimating TED accurately is remarkable and meaningful.