Nonlinear characteristics of silicon resonant accelerometer with vibrating beam integrated with comb fingers structure

Meng-xia LIU; Jian CUI

doi:10.3788/OPE.20202805.1066

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Nonlinear characteristics of silicon resonant accelerometer with vibrating beam integrated with comb fingers structure

Micro/Nano Technology and Fine Mechanics | 更新时间：2020-07-09

- Nonlinear characteristics of silicon resonant accelerometer with vibrating beam integrated with comb fingers structure
- Optics and Precision Engineering Vol. 28, Issue 5, Pages: 1066-1074(2020)
- 作者机构：
  
  北京大学微电子研究所微米/纳米加工技术国家级重点实验室，北京 100871
- 作者简介：
- 基金信息：
- DOI：10.3788/OPE.20202805.1066
  CLC： TH824.4
- Received：03 December 2019，
  
  Revised：09 January 2020，
  
  Accepted：09 January 2020，
  
  Published：15 May 2020
- 稿件说明：
移动端阅览
Meng-xia LIU, Jian CUI. Nonlinear characteristics of silicon resonant accelerometer with vibrating beam integrated with comb fingers structure[J]. Optics and precision engineering, 2020, 28(5): 1066-1074.
DOI：

Meng-xia LIU, Jian CUI. Nonlinear characteristics of silicon resonant accelerometer with vibrating beam integrated with comb fingers structure[J]. Optics and precision engineering, 2020, 28(5): 1066-1074. DOI： 10.3788/OPE.20202805.1066.

摘要

硅微谐振式加速度计的非线性振动可以导致振动幅度噪声耦合到频率输出进而恶化器件的噪声性能，因此有必要对谐振式加速度计的非线性振动特性进行评估及优化，拓展线性振动范围。本文针对所设计的基于梳齿结构与振动梁复合的硅微谐振式加速度计进行了仿真与实验分析。首先对加速度计结构使用COMSOL仿真软件进行了非线性仿真分析，该方法通过在谐振梁的振动方向上施加一个静力，得到力与位移之间的关系，计算出非线性三次项系数

3，eff

和线性系数

eff

的比值约为2.13×10

-2

。然后，对双端固支音叉(DETF)进行扫频测试，得出DETF的非线性振动频响曲线。根据Duffing方程对实验数据进行拟合，得出器件两个DETF的非线性三次项系数

3，eff

和线性系数

eff

的比值分别为2.24×10

-2

和2.19×10

-2

。仿真值与测试值的误差分别为5.2%和2.8%。实验结果与仿真值吻合得较好，印证了仿真方法的有效性和测试数据的可靠性。最后，对所设计的谐振加速度计进行非线性分析，当振幅小于35.4 nm时，DETF工作在线性区，可为后续谐振式加计的控制电路设计提供参考。

Abstract

The nonlinear vibration of the silicon micro-resonator accelerometer can cause the vibration amplitude noise to couple to the frequency output and deteriorate the noise performance of the device. Therefore

it is necessary to evaluate the nonlinear vibration characteristics of the resonant accelerometer and optimize the design to extend the linear vibration range. In this paper

the simulation and experimental analysis of a Silicon micro-Resonant Accelerometer (SRA) based on comb-tooth structure and vibration beam were designed. Firstly

the nonlinear simulation analysis was carried out on the accelerometer structure using COMSOL simulation software. By applying a static force in the vibration direction of the resonant beam

the relationship between force and displacement is obtained

and the nonlinear cubic term coefficient

eff

was calculated. The ratio of

eff

to the linear coefficient

eff

is approximately 2.13 × 10

-2

. Then the Double-End fixed-duty Tuning Fork (DETF) was subjected to frequency sweep test to obtain the nonlinear vibration frequency response curve of DETF. According to the Duffing equation

the experimental data is fitted. The ratio of the nonlinear cubic term coefficient

eff

and the linear coefficient

eff

of the two DETFs of the device is 2.24×10

-2

and 2.19×10

-2

. The errors between the simulated and tested values for

eff

and

eff

are 5.2% and 2.8%

respectively. The experimental results agree well with the simulated values

which confirm the validity of the simulation method and the reliability of the test data. The designed resonant accelerometer was analyzed nonlinearly when the amplitude was less than 35.4 nm

DETF works in the linear region

which can provide reference for the design of the control circuit of the subsequent resonant add-on.

关键词

Keywords

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