题目：薄膜体声波谐振器振动频率分析

摘要：

无线通讯终端的多功能化对射频器件提出了微型化、高频率、高性能、低功耗、低成本等技术要求。薄膜体声波谐振器 (Film Bulk Acoustic Resonators, FBAR) 技术是近年来随着加工工艺技术水平的提高和现代无线通讯技术发展，尤其是随着个人无线通信技术的快速发展而出现的新一代射频器件技术，具有与电路兼容性良好、体积小并且频率相对较高等优良特点。

由于薄膜体声波谐振器技术复杂性以及对性能良好的产品的需求，在加工薄膜体声波谐振器之前对薄膜体声波谐振器进行全面分析以确定材料厚度、振动频率以及电路参数就显得非常自然且有必要。基于薄膜体声波谐振器的层状结构，我们xx可以将其简化为一维无限大层状薄膜板结构。这样，我们就可以对其厚度拉伸和厚度剪切这两个主要工作模态振动频率进行分析。通过给定层状薄膜板的材料常数和厚度，我们可以从频率方程中求解出其振动频率。通过这样的分析得到的计算结果不但与实验测量值相吻合，而且为进一步的分析奠定了基础。将计算公式拓展到考虑压电薄膜的压电效应后，电场就被加入到了原有的分析之中。这样，一方面我们可以分析压电薄膜的压电性质对厚度拉伸和剪切振动频率影响，另一方面也为我们计算电路参数做好了铺垫。

在计算电路参数分析中，材料粘性的引入使得我们利用前期分析结果来计算电路参数成为可能。处理材料粘性的一般办法是将粘性项作为虚数部分插入到本构关系中，从而使得原来的弹性常数转变成了复弹性常数。这样我们就可以在不改变运动方程形式的情况下对电路参数进行计算。目前仍没有合适的方法得到谐振器中常用材料的粘性值，所以我们事先做了假定，在此基础上再计算谐振器中电路参数。之后，我们再将得到的电路参数值与实测的电路参数进行比较最终找到合适的粘性值。

    我们所提供的理论方法可以使谐振器设计者和加工者在产品设计初期就可以估算薄膜厚度和电路参数以设计出合适的振动频率，从而达到{zy}化设计的目的。当然，我们建立的薄膜体声波谐振器分析方法为进一步的有限元分析打下了坚实基础。

英文题目：The Analysis of Vibration Frequency of Film Bulk Acoustic Resonators

英文摘要：

The wireless communication technology demands for RF components of smaller size, high frequency, high performance, low energy consumption, and low cost.  Film bulk acoustic resonators (FBAR) are the latest technology offering RF components of small size and high frequency to the fast growing personal wireless communication technology.

With the sophistication of the FBAR technology and demands for precision products, it is natural to make use of the full analysis of acoustic waves propagating in FBAR structures for design and calculating electrical parameters before the fabrication.  Based on the justified assumption that the layered microstructure of FBAR can also be treated as infinite plates, vibration frequencies of the thickness-extension and thickness-shear vibration modes are calculated from layered models with perfectly bonded interfaces.  A transcendental equation is used to determine the vibration frequency with given materials and plate thicknesses.  By expanding the formulation to include the piezoelectric effect, we shall also be able to obtain the electrical field as a vital addition to mechanical vibration solutions.  Of course, the piezoelectric effect will also be included in the frequency and displacements.  The solutions can be used to calculate the electrical circuit parameters of a resonator.

For electrical circuit parameters, the introduction of material viscosity will enable the formulation and calculation of FBAR properties with solutions of wave propagation.  One approach to treat material viscosity is to assume the elastic constants as complex constants, in which the real part is the elastic constant and the imaginary part is the viscosity that is related to the frequency.  In the mean time, the governing equations should be kept unaltered. However, since the viscosity constants of the film material are not available, so the viscosity of each material can be assumed to enable the calculation of the electrical parameters.  The results can be compared with the measured electrical parameters, such as the quality factor.  Then, a reasonable estimation of the viscosity of the film meterials can be obtained.

The theoretical approach we present here will provide the first step for precise estimation of the thickness and electrical parameters so as to obtain the design frequecy.  Of course, these one-dimensional formulation based on the infinite plate assumption can be further improved through the consideration of finite plates and numerical solutions based on the commonly used finite element analysis.

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