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对于声表面波而言温度特性是非常重要的一个指标.而石英基板在表面波器件中应用广泛.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.在本文中,我们对LeeandYong的理论加以推广,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-切,MD-切和K-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.
For SAW temperature characteristics is a very important indicator.While the quartz substrate in the surface wave device is widely used.When the ambient temperature changes, the substrate size will change, the elastic coefficient and the piezoelectric coefficient will change, The temperature characteristics of the surface acoustic wave device can be examined on the basis of these changes, which is the usual method, but the temperature coefficient of the elastic coefficient and the piezoelectric coefficient actually refers to the intermediate state with temperature change and does not define the elastic coefficient And the reference temperature of the piezo-electric coefficient In some cases, the above-mentioned method will fail due to the temperature variation resulting in a non-uniform distribution of deformations, such as a bulk wave resonator with electrodes and a multilayer surface acoustic wave substrate In other cases, such as force and acceleration sensors, the initial deformation may be due to external forces or accelerations.Some scholars develop a set of nonlinear equations to obtain the propagation characteristics of these small amplitude acoustic waves in the deformed media Theory. According to this theory, you can get the same reference state reference elastic constants and their temperature coefficient .PCYLee YK Yong [Journal of Applied Physics, 1986, 60: 23327] gives a complete set of theories for the small-amplitude vibration of thermomechanical media and derives the first-, second-, and third-order temperature coefficients of quartz crystal elastic constants . They successfully examined the temperature characteristics of quartz wave resonators. In this paper, we extend the theory of Lee and Yong by introducing piezoelectricity, so that the method can also be used to analyze substrates with strong piezoelectricity . We analyzed the temperature characteristics of SAW on quartz substrates. The calculation results of ST-cut, MD-cut and K-cut quartz substrates are given. The calculation results show the effectiveness of the method. Of course, Because this method is theoretically general, if the initial strain distribution in the device structure is calculated first, it can smoothly analyze the operating characteristics of the surface acoustic wave on the multilayer substrate or the sensor performance .