利用时域差分法对薄膜体声波谐振进行二维分析

南京大学学报(自然科学版) ›› 2013, Vol. 49 ›› Issue (1): 40–45.

利用时域差分法对薄膜体声波谐振进行二维分析

曹明，于小利，罗中涌，公勋，章德

出版日期:2015-09-28 发布日期:2015-09-28
作者简介: (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)
基金资助:
National Natural Science Foundation of China(10974094)

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

Cuo Ming ,Yu Xiao一Li ,Luo Zhong-Yong ,Gong Xun**，Zhang De

Online:2015-09-28 Published:2015-09-28
About author: (Key Laboratory of Modern Acoustics(Nanjing University)，Ministry of Education,lnstitutc of Acoustics
Department of Acoustic Science and Enginecring,College of Physics,Nanjing University,
Nanjing, 2 10093 , China)

摘要/Abstract

摘要： 和表面波器件相比，薄膜体声波谐振(FEAR)器件重量轻、尺寸小、成木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.木文中，FI}’I}I}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(PMI.)边界条件被用于实现两侧的吸收边界.在空
气一铝和空气一氮化铝界面上，自由边界条件在FDTD方案中得以实现.另外，在铝一氮化铝内部边界
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. 2 ?m,0. 3 ?m,0. 4 ?m,0. 5 ?m和0. 6 ?m情况卜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. 2 ?m增加到0. 4 ?m逐渐增强.可是，当电极厚度增加到0. 5?m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3?m时，最佳电极厚度应该在0. 4 ?m.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.

Abstract: Film bulk acoustic resonator(FBAR) devices arc lighter, smaller, cheaper and capable of dealing with larger
power than surface acoustic wave devices. In this paper, the finitrdifference timrdomain method(FDTD) is applied to
analyze the thirrfilm 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 arc calculated. Because of the energy-trapping effect,the vibration strength of the
fundamental resonance increases with the electrode thickness varying from 0. 2 ?m to 0.4 ?m. However,when the thickness
increases to 0. 5?m,thc 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 a-
bout 0.4 ?m when AlN film is 3?m thick is recommended. Simulation results show that the FDTD method can be used to
analyze various FBAR structures efficiently.

曹明，于小利，罗中涌，公勋，章德
. 利用时域差分法对薄膜体声波谐振进行二维分析[J]. 南京大学学报(自然科学版), 2013, 49(1): 40–45.

Cuo Ming ,Yu Xiao一Li ,Luo Zhong-Yong ,Gong Xun**，Zhang De. Two-dimensional analysis of film bulk acoustic resonator by
using finite-difference time-domain method*
[J]. Journal of Nanjing University(Natural Sciences), 2013, 49(1): 40–45.

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