利用时域差分法对薄膜体声波谐振进行二维分析(英文)  

Two-dimensional analysis of film bulk acoustic resonator by using finite-difference time-domain method

作　　者：曹明 于小利 罗中涌 公勋 章德 

机构地区：[1]近代声学教育部重点实验室,南京大学声学所,南京大学物理学院声科学与工程系,南京210093

出　　处：《南京大学学报（自然科学版）》2013年第1期40-45,共6页Journal of Nanjing University（Natural Science）

基　　金：National Natural Science Foundation of China(10974094)

摘　　要：和表面波器件相比,薄膜体声波谐振(FBAR)器件重量轻、尺寸小、成本低而且能够处理的功率大.因此,FBAR技术被认为是能够满足现代移动通信系统滤波要求的最有竞争力的技术.对FBAR器件进行模拟的方案中,Butterworth-van Dyke(BVD)模型被广泛应用,但是它不可能被用于分析FBAR的复杂结构.为了准确模拟FBAR器件,必须用到数值方法,如有限元法(FEM)或者时域有限差分(FDTD)法.本文中,FDTD法被用于对薄膜体声波谐振进行二维分析.压电方程和牛顿方程在时间域和空间域中通过中间有限差分进行离散化.完全匹配层(PML)边界条件被用于实现两侧的吸收边界.在空气-铝和空气-氮化铝界面上,自由边界条件在FDTD方案中得以实现.另外,在铝-氮化铝内部边界附近,通过对材料常数取两侧的平均值的方式,实现了连续边界条件,保证了数值计算的稳定性.一款静电场模拟软件ANSOFT Maxwell 2D被用于计算电场强度的分布.当FBAR被外加电压驱动,而电压为时间的正弦函数时,FBAR的输出电流可以表示为一系列正弦函数之和.这些正弦函数中包含了顺态解和稳态解.找出稳态解,就可以计算响应工作频率时的FBAR阻抗特性.文中给出了在不同电极厚度如0.2μm、0.3μm、0.4μm、0.5μm和0.6μm情况下阻抗特性的计算结果.由于能陷效应,基频谐振强度随着电极厚度从0.2μm增加到0.4μm逐渐增强.可是,当电极厚度增加到0.5μm谐振强度又开始减弱.这个现象可以归因于电极的质量负载效应.质量负载会降低谐振强度.通过模拟结果,当氮化铝膜厚度在3μm时,最佳电极厚度应该在0.4μm.我们利用FDTD法对FBAR进行了二维分析.模拟结果显示,FDTD法是分析各种FBAR结构的有力工具.Film-bulk acoustic resonator（FBAR）devices are lighter, smaller, cheaper and capable of dealing with larger power than surface acoustic wave devices. In this paper, the finite-difference time-domain method（FDTD）is applied to analyze the thin-film bulk acoustic wave resonators two-dimensionally. When the FBAR is driven by an externally applied voltage which is a sinuous function of time,the output current can be expressed as a series of sinuous functions of time. The steady solution is selected from the series of sinuous function. The frequency domain electrical impedance characteristics of FBAR with different electrode thicknesses are calculated. Because of the energy-trapping effect, the vibration strength of the fundamental resonance increases with the electrode thickness varying from 0.2μm to 0.4μm. However,when the thickness increases to 0.5 μm,the resonance strength begins to decrease. This phenomenon can be due to the large massloading effect of the electrode which influences the activity of the resonance. From the simulation results, the optimal electrode thickness about 0.4μm when A1N film is 39m thick is recommended. Simulation results show that the FDTD method can be used to analyze various FBAR structures efficiently.

关 键 词：薄膜体波谐振器 时域有限差分法 完全匹配层 

分 类 号：O484.1[理学—固体物理]