层合薄膜电容式微加工超声换能器(CMUTs)谐振频率分析  

Resonant Frequency Analysis of Capacitive Micromachined Ultrasonic Transducers (CMUTs) with Layered Membranes

作　　者：李支康 赵立波[1,2,3,4] 李杰[1,2,3,4] 赵一鹤 徐廷中 罗国希[1,2,3,4] 李雪娇 郭帅帅 蒋庄德 LI Zhikang;ZHAO Libo;LI Jie;ZHAO Yihe;XU Tingzhong;LUO Guoxi;LI Xuejiao;GUO Shuaishuai;JIANG Zhuangde(State Key Laboratory for Manufacturing Systems Engineering,Xi'an Jiaotong University,Xi'an 710049;International Joint Laboratory for Micro/Nano Manufacturing and Measurement Technologies,Xi'an Jiaotong University,Xi'an 710049;School of Mechanical Engineering,Xi'an Jiaotong University,Xi'an 710049;Xi'an Jiaotong University Suzhou Academy,Suzhou 215123)

机构地区：[1]西安交通大学机械制造系统工程国家重点实验室,西安710049 [2]西安交通大学微纳制造与测试技术国际合作联合实验室,西安710049 [3]西安交通大学机械工程学院,西安710049 [4]西安交通大学苏州研究院,苏州215123

出　　处：《机械工程学报》2019年第24期11-20,共10页Journal of Mechanical Engineering

基　　金：国家重点研发计划(2016YFB1200100);国家自然科学基金(51805423,51875449,91748207);苏州市重点产业技术创新-前瞻性应用研究(SYG201721);中国博士后科学基金(2017M623160);机械系统与振动国家重点实验室课题(MSV201809)资助项目

摘　　要：电容式微加工超声换能器(Capacitive micromachined ultrasonic transducers, CMUTs)在3D超声成像、水下超声等领域具有重要应用价值。谐振频率决定着超声成像的分辨率,是CMUTs结构设计的重要参数之一。针对具有多层圆形薄膜的CMUTs结构,提出其薄膜结构和材料参数以及有效电极距离的等效方法,建立在直流偏置电压和交流电压共同作用下多层圆形薄膜的振动方程,并分别采用伽辽金法和能量等效法进行求解,获得多层薄膜CMUTs在偏置电压作用下的两类谐振频率解析式。基于有限元模型,利用数值解来验证谐振频率解析式的正确性,并开展参数化研究。结果显示,基于能量等效法的谐振频率解析式比基于伽辽金法的谐振频率解析式具有更高分析精度,适用于薄膜直径/厚度比在20~100范围内、空腔高度/薄膜厚度比不大于1的多层薄膜CMUTs的谐振频率分析;在从0V到接近于塌陷电压的几乎整个偏置电压变化内,解析解与有限元仿真结果的相对误差小于5%。此外,利用所加工的具有三层薄膜的CMUTs芯片对谐振频率解析式进行试验验证,结果显示在不同偏置电压下谐振频率的试验测试值与理论分析值基本一致。因此,所提谐振频率的理论分析方法可广泛应用于多层薄膜CMUTs结构的设计与优化。Capacitive micromachined ultrasonic transducers(CMUTs) show important applications in fields of 3D ultrasound and underwater imaging. The resonant frequency is one of the important performance parameters of CMUTs, which determines the imaging resolution. For CMUTs with multilayer circular membranes, the calculation methods for the equivalent structure and material property parameters of the multilayer membranes as well as the equivalent electrode distance are proposed. As such, the vibrating equation of the multilayer membranes under both DC bias and AC voltages is established. Both Galerkin method and energy equivalent method are utilized to solve the vibrating equation, and two types of analytical expressions for the resonant frequency are obtained. The numerical results based on finite element method(FEM) are used to validate the analytical expressions, and parametric study for the analytical expressions is further conducted. The results indicate that the analytical expression based on the energy equivalent method has higher accuracy in resonant frequency predication than the one based on the Galerkin method. The theoretical expression is applicable to the cases where the membrane diameter to its thickness ratio is in the range from 20 to 100, and the cavity height is less than or equal to the thickness of CMUTs membranes. The relative error of the theoretical analysis is within 5% with respect to the FEM simulation in almost the whole varying range of the bias voltages, i.e. from 0 V to the voltage closed to the collapse voltage. In addition, CMUTs with three layers of membranes are employed to experimentally validate the analytical expression. The results show that the experimental value of the resonant frequencies of the fabricated CMUTs chips under different bias voltages agree well with the theoretical value by the analytical expression. Therefore, the derived analytical expression for the resonant frequency can be widely used for the design and optimization of CMUTs with multilayer membranes.

关 键 词：CMUTs 多层薄膜 振动方程 能量等效法 谐振频率 解析式 

分 类 号：TH77[机械工程—仪器科学与技术]