Resonances and energy trapping in AT-cut quartz resonators operating with fast shear modes driven by lateral electric fields produced by surface electrodes

Energy-Trapping Characteristics of Lateral Field Excited GdCOB Crystal Bulk Acoustic Wave Devices Based on Stepped Electrodes

In this work, high-frequency forced vibrations of lateral field excitation (LFE) devices with stepped electrodes based on monoclinic crystals GdCOB are modeled, and the influence laws of the device parameters (the step number, size, and thickness of the stepped electrodes) on the energy-trapping effects of the device are revealed. The results show that the step number has a significant effect on the energy-trapping effect of the device: with the increase in the step number, the stronger energy-trapping effect of the device can be obtained; with the increase in the thickness difference of two layers of electrodes, the energy-trapping effect of the device becomes stronger; with the increase in the difference of the electrode radius, the energy-trapping effect of the device is enhanced gradually. The results of this work can provide an important theoretical basis for the design of stepped-electrode LFE resonators and sensors with high-quality factors based on monoclinic crystals.

Stepped electrode designs of TSM langasite resonators for high-temperature applications

In this paper, we report the simulation and fabrication of thickness-shear mode langasite resonators with stepped elliptical electrode designs to investigate their effects on energy trapping and suppression of spurious modes at elevated temperatures. Finite element analysis was conducted to analyze the design of a stepped elliptical electrode on a contoured langasite crystal. Based on the simulation findings, langasite resonators with stepped electrodes were fabricated, and their displacement profiles and frequency-temperature properties were characterized using network analysis and laser Doppler vibrometry. Results demonstrate improved frequency separation between the resonant and spurious modes, and enhanced spurious mode suppression at both room and higher temperatures, suggesting that stepped elliptical electrode designs can effectively enhance the sensing performance of langasite resonators.

Compact liquid analyzer based on a resonator with a lateral excitation electric field

A compact hardware-software complex for measuring the electrical and mechanical parameters of a liquid based on a piezoelectric resonator with a lateral exciting electric field has been developed. It is shown that the modulus of the electrical impedance of the resonator near the resonant frequency decreases monotonically with an increase in conductivity of the contacting liquid. The obtained dependences can be used as calibration curves for measuring conductivity in the range of 100-10,000 μS/cm. A method for the simultaneous determination of the modulus of elasticity, viscosity, and permittivity of a liquid using the electromechanical equivalent scheme was developed and tested on a mixture "water - glycerol" with the different glycerol content.

Uniformization of Mass Sensitivity Distribution of Silver Electrode QCM

Quartz crystal microbalance (QCM) is a highly sensitive mass sensor and has been widely used in many fields. However, the nonuniform distribution of mass sensitivity will lead to poor reproducibility of QCM, which is not conducive to the application of QCM in some fields. Considering the effect of electrode shape, size, and material on mass sensitivity distribution, we found that for an AT-cut QCM with a fundamental frequency of 10 MHz, when the inner and outer diameters of silver ring electrode and the electrode loading factor are 2 and 5 mm and 0.0033, respectively, an approximately uniform mass sensitivity distribution can be obtained. The plating experiment in which rigid silver films were plated on the surface of electrode verified the uniformity. The uniform mass sensitivity distribution will make the application of QCM more convenient; the reproducibility can also be improved. This design of QCM will enrich QCM products and facilitate the application of QCM in various fields.

Sensor Based on PZT Ceramic Resonator with Lateral Electric Field for Immunodetectionof Bacteria in the Conducting Aquatic Environment

A biological sensor for detection and identification of bacterial cells, including a resonator with a lateral electric field based on PZT ceramics was experimentally investigated. For bacterial immunodetection the frequency dependencies of the electric impedance of the sensor with a suspension of microbial cells were measured before and after adding the specific antibodies. It was found that the addition of specific antibodies to a suspension of microbial cells led to a significant change in these frequency dependencies due to the increase in the conductivity of suspension. The analysis of microbial cells was carried out in aqueous solutions with a conductivity of 4.5-1000 μS/cm, as well as in the tap and drinking water. The detection limit of microbial cells was found to be 103 cells/mLand the analysis time did not exceed 4 min. Experiments with non-specific antibodies were also carried out and it was shown that their addition to the cell suspension did not lead to a change in the analytical signal of the sensor. This confirms the ability to not only detect, but also identify bacterial cells in suspensions.

Influence of the conductivity of a liquid contacting with a lateral electric field excited resonator based on PZT ceramics on its characteristics

The influence of the conductivity of a liquid contacting with a piezoelectric resonator with a lateral electric field based on a PZT piezoceramic plate was experimentally and theoretically investigated. In this resonator the shear component of the mechanical displacement, which does not lead to radiation losses upon contact with the liquid, was prevalent. The frequency dependences of the real and imaginary parts of the electrical impedance of the resonator in the frequency range 50-300 kHz showed the presence of three resonances at frequencies of 68.7, 97.8 and 264 kHz with the values of the electro-mechanical coupling coefficient of 12.2%, 14.7% and 6.5%, respectively. The quality factor of each resonance in contact with the liquid turned out to be significantly higher than the quality factor of the resonator with a longitudinal acoustic wave based on lithium niobate. The dependences of the maximum value of the real part of the electrical impedance of such a resonator on the conductivity of the liquid for each resonance were obtained. This experimental data turned out to be in a good agreement with theoretical results obtained by using the method of equivalent circuit.

The sensor for measuring the micro-displacements based on the piezoelectric resonator with lateral electric field

Theoretical and experimental studies of the influence of a thin metal film on the characteristics of a piezoelectric resonator with a lateral electric field showed the possibility of creating a micro-displacement meter in the range of 10-300 μm. For the experiments, two resonators based on the plates of PZT piezoceramics with a thickness of 3.56 and 4.46 mm with resonant frequencies of ~96 and ~260 kHz for both resonators were used. It has been experimentally established that in both cases, with an increase in the width of the gap between the free side of the piezoelectric resonator and thin aluminum film, the frequency of the parallel resonance and maximum value of the real part of the electrical impedance increase and reach saturation. Besides, it has been shown that the relative change of these values with a change in the width of the gap in the range 10-300 μm increases with decreasing the thickness of the resonator. In this case, the frequency of the series resonance practically does not change. It has been also established that the sensitivity of the resonator to the presence of a conducting film at the resonant frequency of ~96 kHz is significantly higher in comparison with the resonant frequency of ~260 kHz. The experimental results are in the qualitative agreement with the theoretical data.

The effect of the conductivity of a film located near a piezoelectric resonator with a lateral electric field based on the PZT ceramics on its characteristics

In this paper, we investigated theoretically and experimentally the effect of the conductivity of the film located in the immediate vicinity of the free side of a piezoelectric resonator based on the PZT ceramics on its characteristics. It is shown that with increasing the conductivity of the film at first the parallel resonant frequency does not change, then it decreases in a certain interval and after that remains practically constant. With increasing the width of the gap between the film and the resonator, the resonant frequency increases and reaches the saturation. At that the degree of the total frequency change decreases with decreasing the conductivity of the film. We also investigated the dependence of the maximum value of the real part of the electrical impedance on the film conductivity at the different values of the width of the gap between the film and the resonator. The dependences of the maximum value of the real part of the electrical impedance on the width of the gap between the film and the resonator are also obtained for different values of the film conductivity. A comparison of the theoretical and experimental data showed their good qualitative agreement.

Frequency interferences of two-unit quartz resonator arrays excited by lateral electric fields

The coupled thickness-twist and face-shear vibrations of the lateral-field-excitation (LFE) two-unit resonator array are analyzed, and the frequency interference and shift of LFE resonator arrays are both studied. Different from most of the quartz resonator arrays based on thickness-field-excitation, the resonator array in this study operates with LFE generated by a pair of electrodes on the top surface of the resonator. By using Mindlin's first-order theory of piezoelectric plates, the electrically forced vibrations are analyzed. The effects of various structural parameters on the frequency interference and shift are examined; furthermore, the corresponding mechanisms are discussed. Varying trends of the frequency interference and shift with various structural parameters are verified by the finite element method. The results are crucial for avoiding frequency interferences between two adjacent units in parameter design of the resonator array operating on LFE.

The Exploration and Confirmation of the Maximum Mass Sensitivity of Quartz Crystal Microbalance

After the advent of the quartz crystal microbalance (QCM) technology, various QCM-based sensing systems have got certain applications in many science and technology fields and resulted in dramatic progress in these fields. The core advantage of QCM is its high mass sensitivity which leads to high accuracy and low detection limit. For a QCM, the mass sensitivity is determined by the diameter and thickness of the electrode to a certain extent when the frequency of the quartz wafer is already determined. Theoretical approximate calculation reveals that there is an optimum electrode diameter corresponding to the maximum sensitivity. This is different from the traditional opinion that the smaller the electrode, the higher the mass sensitivity. A plating experiment was carried out using 28 QCMs with different electrode diameters, and the experimental results verified the existence of the optimum diameter. This study is helpful to obtain higher mass sensitivity by optimizing electrode parameters.

The influence of the metal film, placed close to the free side of the piezoelectric lateral electric field excited resonator, on its characteristics

The influence of the width of the gap between the free side of the piezoelectric lateral electric field excited resonator and the metal film placed on the dielectric plate on the frequencies of the parallel and series resonances was experimentally and theoretically studied. The measurements were carried out in the temperature range of 14-45 °C. It has been shown that the change of the gap width from 0 up to 3.5 mm leads to the change of the parallel resonant frequency on 1.3% at the constant temperature. At the same conditions the change of the series resonant frequency does not exceed 0.07%. Theoretical analysis quantitatively confirmed the experimental dependencies of the aforementioned frequencies on the gap width at the room temperature. At that the maximum difference between the theoretical and experimental values of the parallel and series resonant frequencies in all cases does not exceed 1.2%. The obtained results may be used as the basis for the development of the sensors for the measurement of the displacement in the interval of 0.2-2 mm in the temperature range of 15-45 °C.

Composite lateral electric field excited piezoelectric resonator

The novel method of suppression of parasitic oscillations in lateral electric field excited piezoelectric resonator is suggested. Traditionally such resonator represents the piezoelectric plate with two electrodes on one side of the plate. The crystallographic orientation of the plate is selected so that the tangential components of electric field excite bulk acoustic wave with given polarization travelling along the normal to the plate sides. However at that the normal components of field excite the parasitic Lamb waves and bulk waves of other polarization which deteriorate the resonant properties of the resonator. In this work we suggest to separate the source of the HF electric field and resounded piezoelectric plate by air gap. In this case the tangential components of the field in piezoelectric plate do not practically weaken but normal components significantly decrease. This method is realized on the composite resonator having the structure "glass plate with rectangular electrodes - air gap - plate of 128 Y-X lithium niobate." It has been shown that there exist the optimal value of the width gap which ensure the good quality of series and parallel resonances in frequency range 3-4MHz with record values of Q-factor of ∼15,000 in both cases.

Probing the electrical impedance of thin films on a quartz crystal microbalance (QCM), making use of frequency shifts and piezoelectric stiffening

Using a temperature-responsive polymer film as an example, it was shown that a conventional quartz crystal microbalance (QCM) can probe a sample's electrical properties in addition to its thickness and softness. The film's electrical impedance was accessed by alternating between the driving voltage being applied to the front electrode and the back electrode. The opposing electrode was grounded in both cases. In the first configuration, the electrical properties of the sample do have an influence on the resonance frequency because of piezoelectric stiffening. In the second, they do not. Using this scheme, it was monitored how the electrical impedance of a film composed of a mixture of poly-N-isopropylacrylamide and polyvinylalcohol changes when the film swells and deswells.

Forced vibrations of SC-cut quartz crystal rectangular plates with partial electrodes by the Lee plate equations

Lee plate equations for high frequency vibrations of piezoelectric plates have been established and perfected over decades with the sole objective of obtaining accurate predictions of frequency and mode shapes to aid the analysis and design of quartz crystal resonators. The latest improvement includes extra terms related to derivatives of the flexural displacement to provide much accurate solutions for vibrations of the thickness-shear mode, which is the functioning mode of resonators and has much higher frequency than the flexural mode. The improved Lee plate equations have been used in the analysis of high frequency vibrations of quartz crystal plates as an essential step for analysis of AT- and SC-cut quartz crystal resonators after validations with fully electrode quartz crystal piezoelectric plates. In this study, closed-form solutions of free and forced vibrations of SC-cut quartz plates with partial electrodes are obtained. A procedure has been established for the calculation of dispersion relations, frequency spectra, selected vibration modes, and capacitance ratios of forced vibrations. The vibration solutions obtained with the first-order Lee plate equations are proven to be close to solutions from the Mindlin plate equations. It is now clear that both the Mindlin and Lee plate equations can be used in the analysis and design of quartz crystal resonators.