随着智能感知与无线通信技术的快速发展，声表面波(SAW)器件因其高精度、微型化及无线化的特性，成为传感器与通信系统的核心元件，而叉指电极(IDT)作为SAW器件不可或缺的重要组成部分，其结构形状等特征与SAW器件的性能紧密相连。针对可调控SAW器件的迫切需求，本文系统研究叉指电极的理论设计、仿真方法及任意形状电极的声场调控机制，突破传统均匀电极的性能限制，为高性能SAW器件开发提供理论支撑与技术路径。本文主要分为两部分：一是创新性提出将格林函数理论与电荷密度理论相结合的方法，探究任意形状叉指电极的声场分布情况，二是利用SAW器件的设计与仿真方法，计算并分析直线和折线形状叉指电极的声场指标。

任意形状叉指电极设计理论的研究：首先，基于逆压电效应与波干涉原理对叉指电极设计理论与关键参数优化，建立IDT结构参数与器件性能的定量关系，推导单元静电荷密度p_f(x)的傅里叶变换解析式。其次，构建二维界面格林函数模型，结合矩量法与点匹配技术，通过傅里叶变换与柯西留数定理将周期性电极结构转化波数域空间，并分解格林函数为静电、SAW及体声波分量，提出曲边四边形积分变换方法，实现任意形状IDT的电荷密度与声场分布的精确计算。最终利用电场、应力、力学位移与电场强度之间的关联，揭示电极几何形状参数与声场特性的定量关系，扩展复杂电极结构的适用范围，为非均匀电极形状的声场分析提供关键技术路径。  

任意形状电极SAW器件的设计与仿真探究：首先，建立包含等效波速、反射系数、换能系数的COM方程，结合P矩阵级联技术，实现复杂SAW器件的频率响应分析。其次，通过参数化建模优化叉指电阻与电容的计算方法，建立色散函数模型，分析压电SAW器件的频散特性，提出通过有效介电常数模型优化静电荷分布的方法。最后，通过计算不同形状叉指电极的声场特性指标，总结声场分布变化规律，为高频SAW传感器设计提供理论依据。研究表明：(1)等效波速受电极负载影响显著，电极边缘声阻抗的变化Z/Z₀主要是由电极的电负载和质量负载引起；(2)三次渡越回波可通过调整IDT中心距使回波相位匹配，但无法完全消除，传播损耗需通过材料抛光工艺、温度控制及空气负载综合考量，(3)电极长度与宽度的增加均能提升声场强度，并且长度对声压增量调控更灵敏，压电材料LiNbO₃的声压、声压级和声强最大值分别为7.83251Pa、126.35539dB和4.91379×10^-5W/m²；(4)折线结构比直线更易激发高声压，且声压级衰减更平缓；压电材料LiNbO₃因其具有高机电耦合系数的特点，其声压、声压级和声强均显著优于Si和空气，声压峰值最高达14.38335Pa，比直线声压提高83.63%，且声压级的衰减系数得到明显降低，而非压电材料Si声压峰值为10.06021Pa，衰减系数与压电材料LiNbO₃相比相差不大，空气域声压峰值仅为0.00856Pa，且衰减最快；(5)折线结构的LiNbO₃声强增量的平均值为4.445738×10^-6W/m²，远大于直线电极变化长度的增量平均值5.89833×10^-8W/m²，差值为4.38675×10^-6W/m²，相比提升两个数量级，可通过电极形状与材料协同优化实现声强调控。

本文设计的任意形状叉指电极SAW器件在声场调控领域展现出优异性能，有望应用于智能感知、物联网等领域，该方法为灵活设计SAW 器件提供新的思路。任意形状叉指电极的设计理论，为SAW器件的电极设计与制备提供理论基础，未来可进一步拓展至微流控芯片、无线通信模块等领域，推动物联网感知技术向微型化、智能化方向发展。

With the accelerated development of intelligent sensing and wireless communication technology, Surface Acoustic Wave (SAW) devices have emerged as core components in sensor and communication systems due to their high precision, miniaturization, and wireless capabilities. As an indispensable part of SAW devices, the structure and shape of interdigital transducers (IDT) are closely linked to device performance. Addressing the urgent demand for tunable SAW devices, this work systematically investigates the design theory, simulation methods, and acoustic field regulation mechanisms of arbitrary-shaped IDT, breaking through the performance limitations of traditional uniform electrodes. This work provides theoretical support and technical pathways for the development of high-performance SAW devices. The content is divided into two main parts: Firstly, exploring the acoustic field distribution of arbitrary-shaped IDT based on Green’s function method and charge density theory. Secondly, calculating and analyzing the acoustic field indices of straight and broken line-shaped IDT by using SAW device design and simulation methods.

Research on design theory of arbitrary-shaped IDT. First, based on the inverse piezoelectric effect and wave interference principle, a quantitative relationship between IDT structural parameters and device performance was established. The Fourier transform analytical expression of unit static charge density p_f(x) was derived. Second, the two-dimensional interfacial Green’s function model was constructed, combining the method of moments and point-matching technique. Through Fourier transform and Cauchy residue theorem, periodic electrode structures were transformed into wavenumber domain space. The Green’s function was decomposed into electrostatic, SAW, and bulk acoustic wave components. A curvilinear quadrilateral integral transformation method was proposed to achieve precise calculation of charge density and acoustic field distribution for arbitrary-shaped IDT. By analyzing the correlations between electric fields, stress, mechanical displacement, and electric field strength, the quantitative relationship between electrode geometric parameters and acoustic field characteristics was revealed, which expanding the applicability of complex electrode structures and providing a key technical pathway for acoustic field analysis of non-uniform electrode shapes.

Design and simulation of SAW devices with arbitrary-shaped electrodes. First, a COM equation incorporating equivalent wave velocity, reflection coefficient, and transduction coefficient was established. Combined with P-matrix cascading technology, frequency response analysis of complex SAW devices was achieved. Second, parametric modeling was used to optimize the calculation methods for IDT resistance and capacitance. A dispersion function model was established to analyze the frequency dispersion characteristics of piezoelectric SAW devices. An effective permittivity model was proposed to optimize static charge distribution. Finally, by calculating the acoustic field characteristic indices of different-shaped IDT, the variation law of acoustic field distribution was summarized, providing a theoretical basis for high-frequency SAW sensor design. The research results are as follows: (1) Equivalent wave velocity is significantly affected by electrode loading. Changes in acoustic impedance at electrode edges Z/Z₀ are primarily caused by electrical and mass loading of the electrodes. (2) Third-transit echoes can be phase-matched by adjusting the center distance of IDT but cannot be completely eliminated. Propagation loss requires comprehensive consideration of material polishing processes, temperature control, and air loading optimization. (3) Increasing electrode length and width enhances acoustic field intensity, with length demonstrating higher sensitivity for acoustic pressure regulation. The maximum acoustic pressure, sound pressure level (SPL), and sound intensity of  LiNbO₃ reached 7.83251Pa, 126.35539dB, and 4.91379×10^-5W/m²  respectively. (4) broken-line structures are more effective in exciting high acoustic pressure compared to straight structures, with gentler SPL decay. LiNbO₃ leveraging its high electromechanical coupling coefficient, exhibited significantly superior acoustic pressure, peaking up to 14.38335Pa, which represented an 83.63% increase over straight structures. SPL, and sound intensity compared to Si and air. Non-piezoelectric Si achieved an acoustic pressure peak of 10.06021Pa, With a decay coefficient similar to LiNbO₃, air domains showed the lowest acoustic pressure peak, reaching 0.00856Pa. and fastest decay. (5) The average increase in sound intensity of LiNbO₃ with a broken line structure is 4.445738×10^-6W/m², which is much greater than the average value of the length of the straight line variation5.89833×10^-8W/m², with a difference of 4.38675×10^-6W/m². Compared with the increase of two orders of magnitude, sound intensity control can be achieved through the synergistic optimization of electrode shape and material.

The arbitrary-shaped IDT SAW devices designed in this study demonstrate excellent performance in acoustic field regulation, holding promise for applications in intelligent sensing, the Internet of Things, and other fields. The proposed design method provides theoretical guidance for precise design of high-performance SAW devices. In the future, it can be further expanded to fields such as microfluidic chips and wireless communication modules, which promoting the development of Internet of Things sensing technology towards miniaturization and intelligence.

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