Thickness Shear Mode Research Articles

Effects of air resistance on AT-cut quartz thickness-shear resonators

We study theoretically the effects of air resistance on an AT-cut quartz plate thickness-shear mode resonator. Mindlin's two-dimensional equations for coupled thickness-shear and flexural motions of piezoelectric plates are employed for the crystal resonator. The equations of a Newtonian fluid and the equations of linear acoustics are used for the shear and compressive waves in the air surrounding the resonator, respectively. Solutions for free and electrically forced vibrations are obtained. The impedance of the resonator is calculated. The effects of air resistance are examined. It is found that air viscosity causes a relative frequency shift of the order of ppm. When the material quality factor of quartz Q = 10(5), the air viscosity and compressibility both have significant effects on resonator impedance. For resonators with larger aspect ratios the effects of air resistance are weaker, and the effect of air compressibility is weaker than air viscosity.

A lateral field excited (yxl)88° LiTaO3 bulk acoustic wave sensor with interdigital electrodes

In this work, to improve the sensitivity of lateral field excited (LFE) sensors to changes of liquid conductivity, LFE bulk acoustic wave sensors with interdigital electrodes are investigated. LFE bulk acoustic wave on thickness-shear mode is excited successfully by interdigital electrodes on (yxl)88° LiTaO3 and applied in liquid-phase sensor. The electric field direction of LFE (yxl)88° LiTaO3 plates is determined. Based on this, several LFE bulk acoustic wave sensors with interdigital electrodes are designed and fabricated to increase the sensitivity of LiTaO3 LFE sensors. The results show that the (yxl)88° LiTaO3 LFE sensor with interdigital electrodes is 10.9 times and 2.1 times more sensitive to changes in liquid conductivity compared to traditional LFE devices with single gap circular electrodes and Archimedes spiral electrodes, respectively. The results are important for investigating high-sensitivity LFE bulk acoustic wave sensors by using LiTaO3 crystal.

Analysis of Thickness Vibrations of C-Axis Inclined Zig-Zag Multi-layered Zinc Oxide Thin Film Resonators

The free vibrations of a multilayer C-axis inclined zig-zag ZnO thin-film bulk acoustic wave resonator (FBAR) connected to external impedance have been analyzed; the frequency equation and mode shape for this resonator were derived based on the linear piezoelectric theory. The impedance characteristics of the FBAR are derived and compared with previous experimental results. The analytical result shows that as the layer number increases, the thickness shear mode remains stable while the longitudinal mode has shifted to a lower value. Sensitivity analysis has been performed to explain the discrepancy between our analytical result and previous experiment result. The analytical results provide an insight for the multi-layered zig-zag FBAR design and applications.

Acoustic nickel carbonyl assay – proof of principle

In the Mond process, impure nickel is converted to nickel carbonyl by exposure to carbon monoxide at about 70 °C which is, in turn, decomposed back to nickel at about 200 °C. The decomposition reaction can be made to happen on the surface of a sensor where the rate of nickel deposition is used to calculate the concentration of nickel carbonyl in the gas sample. A novel heated sensor based on an SC cut quartz thickness shear mode acoustic resonator operating at 18 MHz with one electrode acting as a thin film heating element has been demonstrated to be capable of quantitatively detecting nickel carbonyl at 6 parts per billion in a timely manner.

Continuous monitoring of bacterial biofilm growth using uncoated Thickness-Shear Mode resonators

Quartz Crystal Microbalances (QCM) were used to nondestructively monitor in real time the microbial growth of the bacteria Staphylococcus epidermidis (S. epidermidis) in a liquid broth. QCM, sometimes referred to as Thickness-Shear Mode (TSM) resonators, are highly sensitive sensors not only able to measure very small mass, but also non-gravimetric contributions of viscoelastic media. These devices can be used as biosensors for bacterial detection and are employed in many applications including their use in the food industry, water and environment monitoring, pharmaceutical sciences and clinical diagnosis. In this work, three strains of S. epidermidis (which differ in the ability to produce biofilm) have been continuously monitored using an array of piezoelectric TSM resonators, at 37 °C in a selective culturing media. Microbial growth was followed by measuring the changes in the crystal resonant frequency and bandwidth at several harmonics. It was shown that microbial growth can be monitored in real time using multichannel and multiparametric QCM sensors.

Energy trapping of thickness-shear and thickness-twist modes in a partially electroded AT-cut quartz resonator

The thickness-shear and thickness-twist vibrations of a finite and partially electroded AT-cut quartz resonator are investigated. The equations of anisotropic elasticity are used with the omission of the small elastic constant c56. An analytical solution is obtained using Fourier series from which the free vibration resonant frequencies, mode shapes, and energy trapping are calculated and examined.

Variation of the vibration profile of piezoelectric resonant sensors with different electrode conductivity at high temperatures

Gas sensors for applications at elevated temperatures provide improved gas selectivity if fabricated using high-temperature stable piezoelectric resonators. The high-temperature and chemical stability of devices based on langasite coated with metal oxide films supports their application at extreme environments. The vibrational behavior of these resonators is influenced by changes in the electrical and mechanical properties of the metal oxide film.Measurements of the spatial distribution of the displacement characteristics of thickness shear mode resonators are realized using a laser Doppler interferometer at high temperatures and oxygen partial pressures (pO2) down to 10−27bar. The pO2 dependent changes of the properties of a CeO2−x sensor film and the influence on the vibration profile of the resonator are determined. At low pO2 the conductivity of the film increases. Due to the design of the device, the increase of the conductivity results in an enlargement of the effective electrode area of up to 18%. This is reflected in a broadening of the vibration profile of the resonator. Impedance spectroscopy provides comparable results for a pO2 dependent increase of the effective electrode area. The influence of the electrode thickness on the vibration profile is investigated and a decrease of the profile width of up to 11% with increasing thickness is demonstrated. The latter is attributed to an increased energy trapping.

Finite element analysis of lateral field excited thickness shear mode film bulk acoustic resonator

PurposeThis paper aims to propose a new model to study the relationship between the acoustic properties of the thickness shear mode (TSM) in lateral field excited (LFE) film bulk acoustic wave resonator (FBAR) and the gap distance of the surface electrodes.Design/methodology/approachIn the finite element analysis, harmonic and modal analyses are performed to obtain the admittance spectrum and determine the mechanical vibration mode. The results are used to modify the ideal model used in the theoretical calculation.FindingsIn the case of LFE FBAR, the acoustic velocity and electromechanical coupling coefficient (K2) of the TSM decreases as the gap distance decreases and there is a compromise between the exciting effectiveness and the acoustic properties.Originality/valueThe paper proposes a new method to study the dependences of the acoustic properties of the lateral field excited FBAR on the gap distances of the surface electrodes through the extraction of the static capacitance based on the finite element simulation results.

Quasi-thickness-shear waves in thin-film piezoelectric resonators of ZnO and AlN with tilted C-Axis

We study the propagation of Lamb waves in a piezoelectric plate of crystals of class 6mm with tilted c-axis. Dispersion relations for waves in ZnO and AlN plates with a few specific tilting angles of the c-axis are obtained. Displacement amplitude and phase angle distributions along the plate thickness are also calculated. It is shown that for certain values of the tilting angle of the c-axis, there exist long waves with a dominating thickness-shear component. The results further support the possibility of thin-film resonators operating with thickness-shear modes.

Surface acoustic load sensing using a face-shear PIN-PMN-PT single-crystal resonator

Pb(In(0.5)Nb(0.5))O(3)-Pb(Mg(1/3)Nb(2/3))O(3)-PbTiO(3) (PIN-PMN-PT) resonators for surface acoustic load sensing are presented in this paper. Different acoustic loads are applied to thickness mode, thickness-shear mode, and face-shear mode resonators, and the electrical impedances at resonance and anti-resonance frequencies are recorded. More than one order of magnitude higher sensitivity (ratio of electrical impedance change to surface acoustic impedance change) at the resonance is achieved for the face-shear-mode resonator compared with other resonators with the same dimensions. The Krimholtz, Leedom, and Matthaei (KLM) model is used to verify the surface acoustic loading effect on the electrical impedance spectrum of face-shear PIN-PMN-PT single-crystal resonators. The demonstrated high sensitivity of face-shear mode resonators to surface loads is promising for a broad range of applications, including artificial skin, biological and chemical sensors, touch screens, and other touch-based sensors.

Correction factors of the mindlin plate equations with the consideration of electrodes [Correspondence

The Mindlin plate theory plays a vital role in the analysis of high-frequency vibrations of quartz crystal resonators in the thickness-shear mode. The coupled equations with an infinite number of vibration modes have been truncated to retain essential modes with strong couplings for simplified analysis, and correction factors have been introduced to ensure exact solutions at cut-off frequencies as part of the validation procedure. Starting from plates without complications, correction factors have also been modified to include electrodes for their mass effect. Such results have been important for higher-order correction factors to ensure accurate consideration of electrodes in AT-cut quartz crystal plates. The findings in this systematic study of correction factors are readily available for the analytical equations with selected modes with strong couplings, and equally convenient for the implementation of the finite element analysis with the Mindlin plate equations.

The fifth-order overtone vibrations of quartz crystal plates with corrected higher-order mindlin plate equations

Higher-order overtone resonators have been widely used in various electronic products for their higher vibration frequencies, which are in the much-needed frequency range beyond the reach of the fundamental mode. However, the existing designs of higher-order overtone resonators and further improvement for meeting more precise requirements are largely based on empirical approaches. As an analytical effort, we have derived the corrected fifth-order Mindlin plate equations with the consideration of electric potential and overtone displacements. The elimination and truncation of the infinite two-dimensional equations has been done to ensure the exact cut-off frequencies of the fundamental, the third-order overtone, and fifth-order overtone thickness-shear modes in comparison with the three-dimensional equations. The frequency spectra are plotted in the vicinity of overtone thickness-shear modes for analysis of couplings and interactions with spurious modes, and the optimal design of quartz crystal blanks for overtone vibrations has been suggested. The equations, solutions, and method will be important in design of the higher-order overtone thickness-shear vibration resonators.

Highly sensitive detection of organophosphorus pesticides by acetylcholinesterase-coated thin film bulk acoustic resonator mass-loading sensor

An acetylcholinesterase-coated thin film bulk acoustic resonator has been developed for the detection of organophosphorus pesticides. The thin film bulk acoustic resonator acts as a robust mass-sensitive transducer for bio-sensing. This device works in thickness shear mode with a resonance at 1.97GHz. The detection is based on the inhibitory effects of organophosphorus compounds on the enzymatic activity of the acetylcholinesterase immobilized on one of the faces of the acoustic resonator. The enzyme reaction in the substrate solution and the inhibitory effect is observed are real time by measuring the frequency shift. The presence of organophosphorus pesticides can be detected from the diminution of the frequency shift compared with the levels found in their absence. The device exhibits linear responses, good reproducibility, simple operation, portability and a low detection limit of 5.3×10−11M for paraoxon. The detection results of organophosphorus pesticide residues in practical samples show that the proposed sensor has the feasibility and sensing accuracy comparable to gas chromatography.

Shear-horizontal vibration modes of an oblate elliptical cylinder and energy trapping in contoured acoustic wave resonators

We study shear-horizontal free vibrations of an elastic cylinder with an oblate elliptical cross section and a traction-free surface. Exact vibration modes and frequencies are obtained. The results show the existence of thickness-shear and thickness-twist modes. The energy-trapping behavior of these modes is examined. Trapped modes are found wherein the vibration energy is largely confined to the central portion of the cross section and little vibration energy is found at the edges. It is also shown that face-shear modes are not allowed in such a cylinder. The results are useful for the understanding of the energy trapping phenomenon in contoured acoustic wave resonators.

Surface load induced electrical impedance shift in relaxor-PbTiO3 crystal piezoelectric resonators

The effect of surface loads on Pb(Mg1/3Nb2/3)O3-PbTiO3 single crystal piezoelectric resonators was studied. Electrical impedance shifts at both resonance and anti-resonance frequencies due to surface loads were recorded for comparison among face-shear mode, thickness-shear mode, and thickness mode resonators. It was observed that electrical impedances of face shear mode resonators exhibited significantly higher sensitivity to surface load changes comparing with other resonators with similar dimensions, because of enhanced energy dissipation in face shear mode resonators, indicating a promising innovative face-shear mode single crystal piezoelectric sensing mechanism.

Characteristics of thickness-shear modes excited by two layers of piezoelectric films in acoustic sensors

The thickness-shear mode (TSM) excited by two layers of (112(–)0) textured hexagonal piezoelectric films are studied to improve the performances of acoustic sensors. The corresponding researches are carried out by the acoustic wave propagation model which considers the effects of the acoustic attenuations. When the acoustic field and electric field satisfy to a special match condition, i.e. the phase variation of TSM at each film equal to π, both piezoelectric layers with opposite polarization directions reduce the first TSM and generate the second TSM with higher frequency and higher quality factor than the first TSM excited by two-layers of piezoelectric films with identical polarization direction. Furthermore, the second enhanced TSM holds a moderate the ratio of the operating frequency to the quality factor. These properties of the TSM are appropriate for improving the mass sensitivity and sensitive resolution of the acoustic sensors in liquid medium. Acknowledgment: This work is supported by National Natural Science Foundation of China (No. 11004099 and 11174142), State Key Laboratory of Acoustics of Chinese Academy of Sciences, and also PAPD of Jiangsu Higher Education Institutions.

DNA aptamer configuration affects the sensitivity and binding kinetics of thrombin

DNA aptamer configuration affects the sensitivity and binding kinetics of thrombinThrombin is serine protease involved in the coagulation cascade, which converts soluble fibrinogen into insoluble strands of fibrin - a matrix of the blood clot formation. Development of the sensitive method of the thrombin detection in nanomolar level is important for clinical practice. In this work we applied acoustic thickness shear mode method (TSM) for study the binding of human thrombin depending on DNA aptamer configuration. We compared sensitivity of detection and binding kinetics of the thrombin to the conventional DNA aptamers and aptamer dimers immobilized at the surface of quartz crystal transducer. We have shown that aptasensors based on aptamer dimers more sensitively detect thrombin. The aptamer-thrombin complexes were also more stable as revealed from equilibrium dissociation constant,KD, that was 4 times lower for aptamer dimers in comparison with conventional aptamers. Determination of motional resistance,Rm, from acoustic impedance analysis allowed us to find important differences in physico-chemical properties of layers formed by conventional aptamers and aptamer dimers.

Five-mode frequency spectra of x3-dependent modes in AT-cut quartz resonators

We study straight-crested waves and vibration modes with variations along the x(3) direction only in an AT-cut quartz plate resonator near the operating frequency of the fundamental thickness-shear mode. Mindlin's two-dimensional equations for anisotropic crystal plates are used. Dispersion relations and frequency spectra of the five relevant waves are obtained. It is found that, to avoid unwanted couplings between the resonator operating mode and other undesirable modes, in addition to certain known values of the plate length/thickness ratio that need to be avoided, an additional series of discrete values of the plate length/thickness ratio also must be excluded.

Locating a weakened interface in a laminated elastic plate

We study thickness-shear (TSh) free vibrations of an unbounded, laminated elastic plate with three layers of different materials. One of the two interfaces is slightly weakened as described by the shear-lag model that allows the displacement to be discontinuous across the interface. A frequency equation is obtained from the linear theory of elasticity. A perturbation solution of the frequency equation is obtained from which the frequency shifts of TSh modes due to the weakened interface can be calculated. It is shown that the frequency shifts of TSh modes of different orders are different, and they satisfy different conditions when different interfaces are weakened. These conditions are obtained which can potentially be used as criteria for determining specifically which interface is weakened.

Characteristics of thickness-shear modes excited by two-layer piezoelectric film in acoustic sensors

The thickness-shear mode (TSM) excited by two-layer, (112¯0)-textured, hexagonal piezoelectric film is studied to improve the performances of the acoustic sensors. The corresponding theoretical model is presented by the acoustic wave propagation theory in multi-layer structure combined with the excitation of TSM in two-layer piezoelectric film with opposite polarization direction. The model considers the effects of the acoustic attenuations in the Akheiser regime and Landau-Rumer regime. The calculated results manifest that, when the phase variation of two-layer piezoelectric film with opposite polarization direction is the same and equals to π, an enhanced second TSM can be excited and the corresponding first TSM is suppressed. The enhanced second TSM has higher resonant frequency and higher quality factor than the first TSM excited by a single- or two-layer piezoelectric film with identical polarization direction, which can be used for improving the mass sensitivity and sensitive resolution of the acoustic sensors in a liquid medium.