| Piezoelectric film resonator is an emerging resonance device for bulk acoustic wave.By virtue of the piezoelectric effect of piezoelectric film,this resonator can resonate at a frequency as high as GHz.It has been widely used as a core frequency controller in aviation,communication,and sensing.Silicon-based piezoelectric film is commonly adopted in piezoelectric film resonators,filters and sensors.Generally,it consists of a silicon substrate,a lower electrode layer,a piezoelectric film layer and a top electrode layer.By changing the caxis orientation,the piezoelectric film can realize two vibration modes: thickness extension,and thickness shear.The different vibration modes can be activated through electrode design,which also helps to improve performance parameters like electromechanical coupling coefficient and device sensitivity.In this paper,the analytical model is established based on Tiersten’s two-dimensional scalar differential equation.The trapped modes were examined by separation of variables,variational method,and perturbational integration.On this basis,the author discussed how to analyze piezoelectric film sensors and filters.The main research contents are as follows:(1)Based on the two-dimensional scalar equation of the silicon-based piezoelectric film structure,the variation of the equation coefficient with the thickness ratio of the film to the silicon-based structure of ZnO and AlN is calculated,and the range of the positive energy notch(the wave equation coefficient is greater than zero)is given,which provides a reference for the design of the structure size of the silicon-based piezoelectric film acoustic devices.(2)The mechanical properties of the silicon-based piezoelectric film resonator with circular electrodes are studied.The displacement variation in the plane of the model in the energy trapping frequency range and the energy trapping law are revealed,which provides a theoretical basis for the design of the device fixing.The vibration characteristics and in-plane modal changes of silicon-based piezoelectric film sensor with ring electrode are studied.The results show that the vibration distribution in the ring electrode can be adjusted by parameter design to make it relatively smooth and avoid the location-dependence of mass measurement.Through the study of the filter with ring-dot electrode structure,the difference and mean of resonance frequency of the first two operating modes under different electrode size,different mass ratio,and different film thickness are given,which provides a reference for the selection of filter center frequency and the design of bandwidth.(3)The theoretical and numerical simulation of the AlN piezoelectric film filter with interdigital electrodes is carried out systematically.It is shown that there are seven energy trapping modes in four pairs of interdigital electrodes in the energy trapping frequency range,and the number of energy trapping modes is very sensitive to the electrode width and other parameters.The energy distribution under the interdigital electrode and the coupling strength between electrode fingers can be adjusted through the design of electrode parameters,which provides a reference for increasing the filter bandwidth.The influence of electrode finger width,thickness,and density on admittance is revealed by finite element simulation.(4)Based on two-dimensional scalar equations,a silicon-based piezoelectric film filter with rectangular ring-rectangular electrodes and interdigital electrodes is studied by variational method.The in-plane changes of resonant frequency and modes in the range of energy trapping frequency are given.The influence and regulation of geometric parameters of the electrode and piezoelectric film on energy trapping modes and resonant frequency are revealed.(5)For an high-overtone bulk acoustic resonator,the high-order modes at the half wavelength in the film are obtained based on the approximate solution of the two-dimensional scalar equation.The calculation result shows that with the increase of the length of the driving electrode,the number of energy trapping modes increases,and the energy trapping effect is sensitive to the length and thickness of the driving electrode and the length of the electrode free coverage area.(6)The mechanical properties of silicon-based piezoelectric film sensors with a nonuniform mass layer are studied by the perturbation integral method.The frequency shift law is revealed.The influence of the mass layer center thickness on the frequency shift is discussed.The results show that the larger the mass layer center thickness is,the larger the frequency shift is.A similar linear relationship exits between the density of mass layer and the frequency shift.The influence of air impedance on frequency shift and energy dissipation is studied.The results show that the frequency shift caused by air impedance is about parts per million,which increases with the increase of electrode size,air density and film thickness.(7)The theoretical model of the fingerprint sensor in thickness-shear mode is established.The study shows that when the surface load is a local or periodic mass layer,the current density under the mass layer is larger,which is sensitive to geometric and physical parameters.It is found that the distribution of surface acoustic impedance can be determined by measuring the current density,which provides a basis for the design of this kind of acoustic sensor. |
