Zhenghua Qian

Wave propagation in piezoelectric layered structures of film bulk acoustic resonators

In this paper, we consider the sandwich structure composed of silicon substrate, piezoelectric layer and electrode layers in the typical structure of FBAR. We assume a special solution in the form of harmonic wave in the piezoelectric layer, and substitute it into the simplified stress equations of motion and the charge equation of electrostatic. A correction to the solution assumed is obtained in order to satisfy these equations. Similarly, a correctional solution assumed in the form of harmonic wave in the silicon substrate can be obtained. We can substitute these correctional solutions into continuity conditions and boundary conditions. The relations of wave number and frequency are obtained. The dispersion curves are calculated from the relation. The frequencies when wave number is zero, the influence of the mass ratio of piezoelectric layer and electrode plate, and the vibration images are discussed further.

Effect of initial stress on propagation behaviors of shear horizontal waves in piezoelectric/piezomagnetic layered cylinders

An analytical approach is taken to investigate shear horizontal wave (SH wave) propagation in layered cylinder with initial stress, where a piezomagnetic (PM) material thin layer is bonded to a piezoelectric (PE) cylinder. Two different material combinations are taken into account, and the phase velocities of the SH waves are numerically calculated for the magnetically open and short cases, respectively. It is found that the initial stress, the thickness ratio and the material performance have a great influence on the phase velocity. The results obtained in this paper can offer fundamental significance to the application of PE/PM composite media or structure for the acoustic wave and microwave technologies.

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.

Bending and free vibration analyses of antisymmetrically laminated carbon nanotube-reinforced functionally graded plates

In this paper, a simple four-variable first-order shear deformation theory is further applied to solve the bending and free vibration problems of antisymmetrically laminated functionally graded carbon nanotube (FG-CNT)-reinforced composite plates. The adopted four-variable theory contains only four unknowns in its displacement field which is less than the Reddy’s first-order theory. The equations of motion are derived from the Hamilton’s principle with the help of specific boundary conditions. Laminated FG-CNT-reinforced plates with different distribution types of carbon nanotube through the thickness are considered. The material properties of individual layer are estimated by using the extended rule of mixture. Analytical solutions of various simply supported antisymmetric cross-ply and angle-ply laminates are given for case study. The effects of carbon nanotube volume fraction, length to width ratio and thickness to width ratio on the non-dimensional fundamental frequency and the central deflection are investigated for antisymmetrically laminated FG-CNT-reinforced plates.

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.

Investigation of quasi lateral-field-excitation on (yxl)-17° LiNbO3 single crystal

Quasi lateral-field-excitation (LFE) on LiNbO3 crystal is investigated both theoretically and experimentally. It is found that when the driving electric field direction is parallel to the crystallographic X-axis of the piezoelectric substrate, (yxl)-17° LiNbO3 LFE bulk acoustic wave devices work on quasi-LFE mode. The experimental results agreed with the theoretical prediction well. The results provide the cut of LiNbO3 crystal for quasi-LFE bulk acoustic wave devices, which is important for designing high performance LFE sensors on LiNbO3 substrates.

Influence of electrical boundary conditions on profiles of acoustic field and electric potential of shear-horizontal acoustic waves in potassium niobate plates

HighlightsBackward wave (BW) vanishes for SH1 wave under metallization of two sides of a plate.Shorting moves BW point appearance to lower frequency and increase it existence range.Wave fields over plate thickness could be controlled by electric boundary conditions. ABSTRACT The profiles of an acoustic field and electric potential of the forward and backward shear‐horizontal (SH) acoustic waves of a higher order propagating in X‐Y potassium niobate plate have been theoretically investigated. It has been shown that by changing electrical boundary conditions on a surface of piezoelectric plates, it is possible to change the distributions of an acoustic field and electric potential of the forward and backward acoustic waves. The dependencies of the distribution of a mechanical displacement and electrical potential over the plate thickness for electrically open and electrically shorted plates have been plotted. The influence of a layer with arbitrary conductivity placed on a one or on the both plate surfaces on the profiles under study, phase and group velocities of the forward and backward acoustic waves in X‐Y potassium niobate has been also investigated. The obtained results can be useful for development of the method for control of a particle or electrical charge movement inside the piezoelectric plates, as well a sensor for definition of the thin film conductivity.

Forced coupling vibration analysis of FBAR based on two-dimensional equations associated with state-vector approach

In our previous work, a system of two-dimensional equations for piezoelectric thin-film acoustic wave resonators (FBAR) has been derived and then successfully applied on the free vibration analysis of a finite FBAR plate. In this paper, we analyzed the forced vibrations of FBAR with alternating voltage applied on its electrodes. The derived two dimensional equations were simplified based on straight-crested wave approximations and were rewritten into matrix formalism by state-vector approach. With the knowledge of matrix function, the state-vector equation was successfully solved. Results of admittance were obtained with the dependence on the driving frequency and the aspect ratio. The obtained figure was compared with the frequency spectra obtained in free vibration analysis. Different aspect ratios and quality factors were taken to study the effects of them on the admittance. It is shown that admittance is highly influenced by mode couplings. Thus the work in this paper will be important for the thorough understanding of the coupling vibration of FBAR and its optimization design.In our previous work, a system of two-dimensional equations for piezoelectric thin-film acoustic wave resonators (FBAR) has been derived and then successfully applied on the free vibration analysis of a finite FBAR plate. In this paper, we analyzed the forced vibrations of FBAR with alternating voltage applied on its electrodes. The derived two dimensional equations were simplified based on straight-crested wave approximations and were rewritten into matrix formalism by state-vector approach. With the knowledge of matrix function, the state-vector equation was successfully solved. Results of admittance were obtained with the dependence on the driving frequency and the aspect ratio. The obtained figure was compared with the frequency spectra obtained in free vibration analysis. Different aspect ratios and quality factors were taken to study the effects of them on the admittance. It is shown that admittance is highly influenced by mode couplings. Thus the work in this paper will be important for the thoroug...