利用形变媒质上小振幅声波理论研究石英基板上 声表面波温度特性

南京大学学报(自然科学版) ›› 2013, Vol. 49 ›› Issue (1): 52–57.

利用形变媒质上小振幅声波理论研究石英基板上
声表面波温度特性

罗中涌，曹明，公勋，章德

出版日期:2015-09-25 发布日期:2015-09-25
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 oI China(10974094)

Investigation of temperature characteristics of surface acoustic waves on quartz
substrates by using theory of small amplitude vibrations in deformed media*

Luo Zhong-Yong，Cuo Ming，Gong Xun**，Zhang De

Online:2015-09-25 Published:2015-09-25
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： 对于声表而波而言温度特性是非常重要的一个指标.而石英基板在表而波器件中应用广泛
当环境温度改变时，基板尺寸会发生变化，弹性系数和压电系数值也会发生变化，在考虑这些变化的基
础上就可以考察声表面波器件的温度特性.这是通常的方法.但是，弹性系数和压电系数的温度系数其
实参考了随温度变化的中间状态，而并非定义弹性系数和压电系数的参考温度时的状态.在某些场合
下，由于温度变化会产生一个非均匀分布的形变，比如带电极的体波谐振器以及多层声表面波基板，上
述方法就会失效.在其它的一些场合，如力和加速度传感器的情况，初始形变可能是由于外力或者加速
度造成的.为了得到这些在形变媒质上小振幅声波的传播特性，一些学者从非线性方程发展出一套理
论.按照这种理论，可以得到参考同一参考状态的弹性常数以及它们的温度系数.P. C. Y. Lee和Y. K.
Yong[Journal of Applied Physics,1986,60;.2327]给出了一套完整的热形变媒质中小振幅振动的理论，
并推导出了石英晶体弹性常数的一阶、二阶和三阶温度系数.他们成功地考察了石英体波谐振器的温度
特性.在木文中，我们对Lee and Yong的理论加以推广’一，引入了压电性.这样，该方法也可以用来分析具
有强压电性的基板了.我们分析了石英基板上声表面波的温度特性.文中给出了ST一切，MD一切和K
一切石英基板的计算结果.计算结果证明了该方法的有效性.当然新方法比传统的方法要复杂的多.因
为该方法在理论上具有一般性，如果先计算出器件结构中初始应变的分布，它就可以顺利地来分析多层
基板上声表面波或者是一些传感器的工作特性.
关键词:石英基板，声表而波，温度特性

Abstract: The temperature characteristics arc important for surface acoustic wave(SAW)devices. And quartz sub-
strates arc very popular for SAW application. Conventionally, when temperature characteristics of SAW arc investi-
gated，the dimensional change due to environmental temperature change is first considered and then the temperature
derivatives of the elastic and piezoelectric constants arc introduced to analyze it. However, the used temperature de-
rivatives of the effective elastic constants arc referred to the variable temperature-dependent intermediate state rather
than the fixed reference state, to which the fundamental elastic constants arc referred.The conventional method can-
not conveniently be employed because temperature change usually leads to initial inhomogencous strain distribution
in the device structure. P. C. Y. Lec and Y. K. Yong have given a complete set of theory for small amplitude vibra-
dons in thermally deformed media.They have successfully applied their theory to investigate the temperature charac-
teristics of bulk wave resonators of quartz.ln this paper,thcir work is further extended to include the piczoclectrici-
ty.The temperature characteristics of SAW on quartz plates arc investigated by using the new method. For the gen-
crality of the present method，given the initial strain distribution in the device structure is calculated first，the new
method is ready for analyzing the multilaycred SAW substrate or sensors.

罗中涌，曹明，公勋，章德 . 利用形变媒质上小振幅声波理论研究石英基板上
声表面波温度特性
[J]. 南京大学学报(自然科学版), 2013, 49(1): 52–57.

Luo Zhong-Yong，Cuo Ming，Gong Xun**，Zhang De. Investigation of temperature characteristics of surface acoustic waves on quartz
substrates by using theory of small amplitude vibrations in deformed media*
[J]. Journal of Nanjing University(Natural Sciences), 2013, 49(1): 52–57.

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