Energy Dissipation Contribution Modeling of Vibratory Behavior for Silicon Micromachined Gyroscope

Received Jan 25, 2018; Accepted Mar 6, 2018

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1. Introduction

Vibration behavior is an important feature of MEMS two-order mass-damping-stiffness system. Energy conversion is a fundamental characteristic of these vibrational system. For some type MEMS devices, vibration regarded as energy is collected as power of electrical components, such as vibration energy harvest [1–3]. For another type devices, this vibration behavior can be localized to improve signal noise ratio (SNR) greatly [4]. Nevertheless, more common but inevitable phenomenon for all of MEMS devices during vibration occurrence is vibration energy dissipation behavior, typically such as micromachined Coriolis vibratory gyroscope (MCVG) [5–7]. The performance of this type of vibration system is significantly limited by the rate at which the vibration energy is dissipated, which is called time constant. $Q$ is generally used as a measurement of this time constant of the vibration energy and is defined as ratio of the total strain energy to the dissipated energy per vibration cycle. Higher $Q$ means larger time constant and lower vibration energy dissipation, for the MCVG, which means achievement of excellent bias stability [8–12].

In order to achieve high performance of the MCVG, analysis of energy dissipation mechanisms of the Q value of the MCVG during vibration becomes an important issue [13–16]. For the single-mode mass-damping-stiffness resonator, the $Q$ value has been widely regarded as a combination of five energy dissipation mechanisms and inverse proportion to the total energy dissipation [17–19]. Energy dissipation usually consists of two categories: intrinsic dissipation such as thermoelastic damping loss 1/Q_the, anchor damping loss 1/Q_anc, and Akhiezer damping loss 1/Q_akh and extrinsic dissipation such as surface damping loss 1/Q_sur and air damping loss 1/Q_air.

These damping loss mechanisms of the single-mode resonators have been extensively investigated for achieving the expected Q. In summary, influencing factors on damping losses can contribute to three aspects: vacuum packaging technology, materials properties, and mechanical structure topology. First, vacuum packaging scheme as the most common one is used to greatly decrease air damping, such as epi-seal encapsulation process [20–25], hermetic...

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