Zinan Zhao

Energy trapping of thickness-extensional modes in thin film bulk acoustic wave filters

This paper presents the thickness-extensional vibration of a rectangular piezoelectric thin film bulk acoustic wave filter with two pairs of electrodes symmetrically deposited on the center of the zinc oxide film. The two-dimensional scalar differential equations which were first derived to describe in-plane vibration distribution by Tiersten and Stevens are employed. The Ritz method with trigonometric functions as basis functions is used based on a variational formulation developed in our previous paper. Free vibration resonant frequencies and corresponding modes are obtained. The modes may separate into symmetric and antisymmetric ones for such a structurally symmetric filter. Trapped modes with vibrations mainly under the driving electrodes are exhibited. The six corner-type regions of the filter neglected by Tiersten and Stevens for an approximation are taken into account in our analysis. Results show that their approximation can lead to an inaccuracy on the order of dozens of ppm for the fundamental mode, which is quite significant in filter operation and application.

Thickness-shear and thickness-twist modes in an AT-cut quartz acoustic wave filter

We studied thickness-shear and thickness-twist vibrations of a monolithic, two-pole crystal filter made from a plate of AT-cut quartz. The scalar differential equations derived by Tiersten and Smythe for electroded and unelectroded quartz plates were employed which are valid for both the fundamental and the overtone modes. Exact solutions for the free vibration resonant frequencies and modes were obtained from the equations. For a structurally symmetric filter, the modes can be separated into symmetric and antisymmetric ones. Trapped modes with vibrations mainly under the electrodes were found. The effect of the distance between the two pairs of electrodes was examined.

Vibration optimization of ZnO thin film bulk acoustic resonator with ring electrodes

A rectangular ZnO thin film bulk acoustic resonator with ringelectrodes is presented in this paper to demonstrate the existence of a nearly uniform displacement distribution at the central part of this typical resonator. The variational formulation based on two-dimensional scalar differential equations provides a theoretical foundation for the Ritz method adopted in our analysis. The resonant frequencies and vibration distributions for the thickness-extensional modes of this ringelectroderesonator are obtained. The structural parameters are optimized to achieve a more uniform displacement distribution and therefore a uniform mass sensitivity, which guarantee the high accuracy and repeatable measurement for sensor detection in an air or a liquid environment. These results provide a fundamental reference for the design and optimization of the high quality sensor.

Effects of unequal electrode pairs on an x-strip thickness-shear mode multi-channel quartz crystal microbalance.

We study the thickness-shear vibrations of an x-strip monolithic piezoelectric plate made from AT-cut quartz crystals with two unequal electrode pairs. The Tiersten-Smythe scalar differential equations for electroded and unelectroded quartz plates are separately employed, resulting in free vibration distributions and frequencies of operating modes. The vibrations of these operating modes are mainly trapped in the electroded regions. The loss of the structural symmetry can lead to a weak vibration interaction between two electroded regions. The influences of electrode difference on the vibration and frequency interference between two adjacent resonators are investigated in detail. The obtained results provide a fundamental reference to the design and optimization of multi-channel quartz crystal microbalance.

Thickness-shear vibration of a Z-strip AT-cut quartz crystal plate with nonuniform electrode pairs

ABSTRACT Thickness-shear vibration of a z-strip AT-cut quartz crystal plate covered by two pairs of electrodes with nonuniform lateral size and thickness is investigated by the Tiersten-Smythe scalar differential equations. Exact modes and resonant frequencies are obtained for different electrode dimensions, which are qualitatively validated by the displacement distribution of the fundamental mode from some existing work. The asymmetric structure results in the loss of the symmetry of the thickness-shear vibration. The effects of geometric parameters and mass ratios on the vibration distributions are discussed in detail, which provides a fundamental reference for the design and application of quartz crystal devices.

Thickness-extensional trapped energy vibration of ZnO thin film bulk acoustic wave filters

Thickness-extensional vibration of a rectangular piezoelectric thin film filter symmetrically covered with two driving electrodes was studied in this paper. The Tiersten and Stevens scalar equation was employed. The Ritz method based on the variational formulation constructed in our previous work was used with trigonometric series as basis functions. Free vibration modes and corresponding resonant frequencies were obtained, which shows that the modes can separate into symmetric modes and anti-symmetric modes for this symmetric structure. Trapped modes with vibration mainly under the top electrode regions were illustrated. The six corner-type regions of the filter neglected by Tiersten and Stevens for simplicity were considered in our analysis. Results show that their approximation may lead to an inaccuracy ranging from dozens to hundreds of ppm for the fundamental symmetric modes, which is severe to filter design and operation.

Analysis of thickness-extensional modes in energy-trapped thin film resonators

A theoretical analysis on a rectangular energy-trapped piezoelectric thin zinc oxide film resonator operating with thickness-extensional modes is performed in this paper. The two-dimensional scalar differential equations derived by Tiersten and Stevens are used which can describe the in-plane mode distribution. Based on the scalar equations, we construct a variational formulation which provides a theoretical foundation for the Ritz method in our analysis. Free vibration frequencies and corresponding mode shapes are obtained and discussed. Modes with vibration mainly under the electroded area are proved to exist. The results show that the classical method with an approximation of neglecting the four corner regions can cause a frequency error on the order of dozens of parts per million for the fundamental thickness-extensional modes, which is significant for the design and operation of the FBARs.