AT-cut Quartz Resonators Research Articles

Theory and experimental verifications of the resonator Q and equivalent electrical parameters due to viscoelastic and mounting supports losses

A novel analytical/numerical method for calculating the resonator Q and its equivalent electrical parameters due to viscoelastic, conductivity, and mounting supports losses is presented. The method presented will be quite useful for designing new resonators and reducing the time and costs of prototyping. There was also a necessity for better and more realistic modeling of the resonators because of miniaturization and the rapid advances in the frequency ranges of telecommunication. We present new 3-D finite elements models of quartz resonators with viscoelasticity, conductivity, and mounting support losses. The losses at the mounting supports were modeled by perfectly matched layers (PMLs). A previously published theory for dissipative anisotropic piezoelectric solids was formulated in a weak form for finite element (FE) applications. PMLs were placed at the base of the mounting supports to simulate the energy losses to a semi-infinite base substrate. FE simulations were carried out for free vibrations and forced vibrations of quartz tuning fork and AT-cut resonators. Results for quartz tuning fork and thickness shear AT-cut resonators were presented and compared with experimental data. Results for the resonator Q and the equivalent electrical parameters were compared with their measured values. Good equivalences were found. Results for both low- and high-Q AT-cut quartz resonators compared well with their experimental values. A method for estimating the Q directly from the frequency spectrum obtained for free vibrations was also presented. An important determinant of the quality factor Q of a quartz resonator is the loss of energy from the electrode area to the base via the mountings. The acoustical characteristics of the plate resonator are changed when the plate is mounted onto a base substrate. The base affects the frequency spectra of the plate resonator. A resonator with a high Q may not have a similarly high Q when mounted on a base. Hence, the base is an energy sink and the Q will be affected by the shape and size of this base. A lower-bound Q will be obtained if the base is a semi-infinite base because it will absorb all acoustical energies radiated from the resonator.

Effects of electromagnetic radiation on the Q of quartz resonators

The quartz resonator Q with aluminum electrodes was studied with respect to its fundamental thickness shear mode frequency and its viscoelastic, viscopiezoelectric, and viscopiezoelectromagnetic behaviors. The governing equations for viscoelasticity, viscopiezoelectricity, and viscopiezoelectromagnetism were implemented for an AT-cut quartz resonator. To simulate the radiation conditions at infinity for the viscopiezoelectromagnetic model, perfectly matched layers over a surface enclosing the resonator were implemented to absorb all incident electromagnetic radiation. The shape of the radiation spectrum of a 5.6 MHz AT-cut quartz resonator was found to compare relatively well the measured results by Campbell and Weber. The mesa-plate resonator was studied for a frequency range of 1.4 GHz to 3.4 GHz. The resonator Q was determined to be influenced predominantly by the quartz viscoelasticity; however at frequencies greater than 2.3 GHz, the quartz electromagnetic radiation had an increasingly significant effect on the resonator Q. At 3.4 GHz, the electromagnetic radiation accounted for about 14% of the loss in resonator Q. At frequencies less than 2 GHz, the calculated resonator Q compared well with the intrinsic Q(x) provided by the formula Q(x) = 16 x 10(6)/f where f was in MHz. At frequencies higher than 2.3 GHz, the aluminum electrodes had significant effects on the resonator Q. At 3.4 GHz, the electromagnetic radiation loss in the electrodes was an order of magnitude greater than their viscoelastic loss; hence, the vibrating aluminum electrodes became an efficient emitter of electromagnetic waves. The effects of electrical resistance in both the electrodes and quartz were determined to be negligible.

Optimal electrode shape and size of a few singly rotated quartz and langasite resonators

Based on Mindlin's early work, we calculate and plot optimal electrode shape and size of Y-cut quartz, At-cut quartz, and Y-cut langasite plate thickness-shear resonators. The electrodes obtained are optimal in that they satisfy Bechmann's number in every direction. The results are useful in the design optimization of these resonators.

A frequency of the quartz crystal microbalance (QCM) that is not affected by the viscosity of a liquid

The Sauerbrey equation, widely used in quartz crystal microbalances (QCM), expresses the relationship between resonance frequency changes and mass load changes. When a QCM is used in a liquid, however, its resonance frequency is known to be affected not just by the mass load but also by the viscous load of the liquid. Using a network analyzer, we analyzed the impedance of an AT-cut quartz resonator. Based on an admittance diagram given by impedance measurements, the series resonance frequency fs, where conductance is at its maximum, and the two frequencies f1 and f2 (f1 < f2), where conductance is half its maximum, were determined and analyzed at the same time. f1 and f2 are frequencies traditionally used when determining the quality factor for quartz. Focusing on these frequencies, we first conducted an experiment using a 27 MHz quartz resonator in which we changed the liquid temperature of de-ionized water from 26 °C to 62 °C. Changes in liquid temperature allowed measurement of the effect of viscosity changes in the de-ionized water on the above frequencies. Results revealed a rise in frequency of about 2500 Hz for fs and about 100 Hz for f2. Next, we measured the effects of each frequency when the liquid was changed to a glycerol concentration of 0–14 wt% and an ethanol concentration of 0–10 wt%. fs was affected by viscosity, which changed due to the rise in concentration. This frequency change coincided for the most part with theoretical values representing the viscous load of the liquid. f2, however, was mostly unaffected by viscosity, which changed as a result of the rise in concentration. Then, we performed measurement with a mixture of avidin and glycerol. The frequency change for fs was about −50 Hz while that for f2 was about −30 Hz. When, as a reference, a solution of avidin alone was added, the frequency change for both fs and f2 was about −30 Hz. When glycerol alone was added, the frequency change for fs was about −25 Hz, but there was no frequency change for f2. Based on theory and the above measurement results, f2 was found to have characteristics that are not affected by the viscous load of a Newtonian liquid. Thus, using f2 for a QCM subject to viscous changes in a liquid allowed more accurate determination of the mass load than fs.

Detection of NH3 by quartz crystal microbalance coated with TiO2

A quartz resonator with a thin TiO2 film is investigated in view of possible applications as a sensor for detecting the presence of ammonia in the ambient. A study of the sorption properties of thin TiO2 films to NH3 vapors is also presented. The films are deposited using electron beam evaporation. In order to determine the sorption ability of TiO2 to NH3, a quartz crystal microbalance (QCM) with a thin TiO2 film is used, the latter serving as a receptor for the NH3 gas. The AT-cut 16-MHz quartz resonator allows conversion of the additional mass load that occurs as a result of sorption into a frequency shift. The experiments are carried out by measuring the QCM resonant frequency shift due to the absorption of vapors from an aqueous solution of NH3 with different concentration ranging from 100 to 1000 ppm. The experimental results obtained indicate that the variation of the resonant frequency is a function of the ammonia concentration. This demonstrates that a QCM covered with a thin TiO2 layer is sensitive to ammonia vapors at room temperature and is capable of detecting NH3 concentrations in the range investigated (100-1000 ppm).

High-Speed Measurement of Mode Shapes and Vibrational Displacement in Piezoelectric Resonators Using Two Lasers with Different Wavelengths

Our new method solves the limitation, that is, the requirement of two measurements with different device driving levels, of the previous system for measuring the in-plane vibrational displacement, using two lasers with adequately separated wavelengths. Different interference factors γs are determined for each speckle image by using the lasers. The ratio of the two γs is proportional to the reciprocal of the wavelength ratio. The distributions of the absolute vibrational displacement can be mapped based on this relationship and statistical processing of the speckle images. Red-and-violet semiconductor lasers were used in the actual measurement system. A 23-MHz circular AT-cut quartz resonator was used to test the validity of our method, and the results are compared here to the results previously obtained by the two-level burst wave excitation method.

Estimation of Quartz Resonator Q and other Figures of Merit by an Energy Sink Method

An important determinant of the quality factor Q of a quartz resonator is the loss of energy from the electrode area to the base via the mountings. The acoustical characteristics of the plate resonator are changed when the plate is mounted onto a base substrate. The base substrate affects the frequency spectra of the plate resonator. A resonator with a high Q may not have a similarly high Q when mounted on a base. Hence, the base is an energy sink and the Q will be affected by the shape and size of this base. A lower bound Q will be obtained if the base is a semi-infinite base since it will absorb all acoustical energies radiated from the resonator. A scaled boundary finite element method is employed to model a semi-infinite base. The frequency spectra of the quartz resonator with and without the base are presented. In addition to the loss of energy via the base, there are other factors which affect the resonator Q, such as, for example, material dissipation, and damping at the interfaces of quartz and electrodes. The energy dissipation due to material damping increases with the resonant frequency and the reduction of resonator size; hence material damping becomes important in the current and future miniaturized resonators operating at very high frequencies. An energy sink model along with material dissipation would provide realistic Q, motional capacitance, motional resistance, and other figures of merit useful for designing resonators. The model could be used for evaluating resonator and mountings designs of microelectromechanical systems and miniaturized devices. The effect of the mountings, and plate and electrode geometries on the resonator Q and other electrical parameters are presented for AT-cut quartz resonators. Model results from the energy sink method were compared with experimental results and were found to be good.

Absolute Measurement of Surface Vibrational Distribution in Piezoelectric Devices Using Burst-Wave Driving

A non mechanical scanning method is developed for mapping absolute vibrational patterns of piezoelectric devices based on a burst-wave resonator drive and the laser speckle method. By taking into account the statistical treatment for the distributions of the speckle intensity, absolute vibrational shapes can be visualized. This method is based on a simple relationship of coherent light interference on device surfaces and the linear relationship of piezoelectricity. To derive the interference factor γ, which is mandatory for determining absolute displacement, a polynomial approximation is applied to an expression of the difference in the brightness caused by the interference condition between the resonator-resting and resonator-driving states. This is because γ cannot be directly obtained from the interference equations when the device being tested is excited by the burst signal. Although the sensitivity of this method is less than that of the synchronized laser speckle method, its simple measurement system and wide frequency range more than offset this disadvantage. An experimental result for a 23 MHz AT-cut quartz resonator is also presented.

Effect of Adding Coils to Dual-Input Twin-T Quartz Circuit

We derived an exact frequency equation and examined the behaviors of the effective Q factor and effective resistance for the case in which coils are added to a dual-input twin-T quartz circuit whose null frequency can be changed by adjusting the applied voltage ratio. In the circuit construction, two sets of T-circuits are used in which a quartz resonator is placed in the shunt branch and the output of each circuit settles in one terminal. The changeable frequency range exceeds the limit determined by the electromechanical coupling factor of the piezoelectric resonator used without any decrease in the effective Q factor and any increase in the effective resistance, within the entire changeable-frequency range when the resonance frequency of a coil and a capacitor in the series branch of the twin-T circuit is set to almost the same value as the resonance frequency of the resonators used in the twin-T circuit. The derived null-frequency equation and effective Q factor agreed with the experimental results for AT-cut quartz resonators.

Frequency Shift of Thickness-Shear Vibrations of AT-Cut Quartz Resonators Due to a Liquid Layer with the Electrode Stiffness Considered

Thickness-shear vibrations of an AT-cut quartz resonator due to a liquid layer are studied. Closed form solutions are obtained with electrodes considered. Effect of the shear stiffness of electrodes on frequency shifts is presented.

Stress-induced frequency shifts in rotated Y-cut langasite resonators with electrodes considered

Stress-induced frequency shifts of the thickness-shear vibration of rotated Y-cut langasite resonators are studied with the electrode considered. The relationship between mass loading and force-frequency coefficients is explored for several kinds of electrode materials. Comparisons between Y-cut langasite and AT-cut quartz resonators are also presented.

Effects of Thermal Stresses on the Frequency-Temperature Behavior of Piezoelectric Resonators

The frequency-temperature behavior of a piezoelectric crystal resonator can be predicted quite accurately if the resonator is under a stress-free and steady-state uniform temperature condition. The condition is however seldom achieved practically. Most practical resonators are subjected to thermal stresses. Conventional finite element analytical tools such as ANSYS cannot provide a sufficiently accurate model for the frequency-temperature behavior of piezoelectric quartz resonators. A new dynamic frequency-temperature model which accurately predicted the frequency-temperature behavior of quartz resonators affected by transient and steady state temperature changes was presented. Lagrangean equations for small vibrational (incremental) displacements superposed on initial thermal stresses and strains were employed. The initial thermal stresses and strains were obtained from the uncoupled heat and thermoelastic equations. The constitutive equations for the incremental displacements incorporated the temperature derivatives of the material constants. Numerical results were compared with the experimental results for a 50 MHz AT-cut quartz resonator mounted on a glass package. Good comparisons between the experimental results and numerical results from our new model were found. The differences between the thermal expansion coefficients of glass and quartz gave rise to the thermal stresses that had adverse effects on the frequency stability of resonators. Different optimal crystal cut angles of quartz, and resonator geometry were found to achieve stable frequency-temperature behavior of the resonator in a glass package. The dynamic frequency-temperature model was used in the theoretical analyses and designs of high Q, 3.3 GHz, quartz thin film resonators.

Lateral field excitation of thickness shear mode waves in a thin film ZnO solidly mounted resonator

In recent years, interest in the development of highly sensitive acoustic wave devices as biosensor platforms has grown. A considerable amount of research has been conducted on AT-cut quartz resonators both in thickness excitation and in lateral excitation configurations. In this report, we demonstrate the fabrication of a ZnO solidly mounted resonator operated in thickness shear mode (TSM) using lateral field excitation of the piezoelectric film. Theoretical Christoffel equation calculations are provided to explore the conditions for excitation of a TSM wave in c-axis-oriented ZnO through lateral excitation. The existence of a TSM wave is verified through the comparison of theoretical and experimentally obtained acoustic velocity values from frequency versus thickness measurements and water loading of the resonators. A major strength of this design is that it incorporates a simple eight-layer, single-mask fabrication process compatible with existing integrated circuit fabrication processes and can be easily incorporated into multidevice arrays. With minimal electrode optimization, we have been able to fabricate resonators with nearly 100% yield that demonstrate Q values of up to 550 and K2 values of 0.88% from testing of more than 30 devices.

Experimental Study of Mode-Coupling Strength of AT-Cut Quartz Resonators with High Mesa Step Height

In this paper, the bi-mesa resonators, which can be fabricated with very high mesa steps, were fabricated, and their frequency-temperature (f-T) characteristics were measured as an index of the mode-coupling strength. Since the mode-coupling affects to the first-order temperature coefficient of the TS-1 mode, the f-T curve of the pure TS-1 mode rotates clockwise depending on the mode-coupling strength. The experimental results showed that the tendency of the first-order coefficients of the measured f-T data were in good agreement with the calculated mode-coupling strength in the mesa height range of 0 to 50%. These results indicate the validity of the calculated mode-coupling strength between TS-1 and TF modes. It is also showed that choosing lower mesa height is desirable because the face-shear modes caused by the X-Z' boundary tend to couple with the TS-1 mode when the mesa step is very high.

Quartz crystal microbalance determination of trace metal ions in solution

Abstract This paper describes studies of a combined electrochemical/acoustic wave sensor for detection of metal ions in aqueous solutions. The sensor is based upon surface complexation of the metal ions at thiodisuccinic acid (TDS) functionalised self-assembled monolayer (SAM) modified electrodes on 10 MHz AT-cut quartz resonators, functioning as a quartz crystal microbalance (QCM). The SAM-modified electrodes were employed for the detection of Cd(II) ions in single and mixed metal ion solutions, with Pb(II) or Cu(II) as the interferants. Acoustic determination was based on the QCM frequency change associated with the binding to the surface-immobilised ligand of metal ions as a function of their concentration. Frequency response data were acquired under emersed and immersed conditions for ligand binding to the Au electrode and, subsequently, metal ion binding to the ligand. In the latter case, the data were interpreted according to a range of isotherms, of which the Temkin isotherm was found empirically best to describe the concentration dependence. The acoustic wave data yielded information on equilibrium binding stoichiometry and energetics. The extent of metal ion binding was also determined by coulometric assay (upon reduction to the zero-valent metal) after transfer to metal ion-free electrolyte solution. XPS studies of surface-bound metal-TDS ligand complexes confirmed the binding stoichiometry obtained from the electrochemical and acoustic wave responses, and provided information on the ligand–substrate binding and bound analyte oxidation state.

Use of single-walled carbon nanotubes to increase the quality factor of an AT-cut micromachined quartz resonator

In this letter, we report the suppression of loss mechanisms in an AT-cut quartz resonator operating in thickness shear mode using an over layer of single-walled carbon nanotubes (SWNTs), and the resulting increase in the Q (quality) factor of the resonator by as much as 100%. The Q factor was found to monotonically increase as more SWNTs were added to the resonator. The increase in the Q factor of the resonators is thought to arise due to suppression of surface loss modes due to interaction of the carbon nanotubes with the quartz resonator surface. The use of SWNTs provides a very effective and simple way to improve the performance of quartz resonators.

Single-walled carbon nanotubes nanocomposite microacoustic organic vapor sensors

We have developed highly sensitive microacoustic vapor sensors based on surface acoustic waves (SAWs) configured as oscillators using a two-port resonator 315, 433 and 915 MHz device. A nanocomposite film of single-walled carbon nanotubes (SWCNTs) embedded in a cadmium arachidate (CdA) amphiphilic organic matrix was prepared by Langmuir–Blodgett technique with a different SWCNTs weight filler content onto SAW transducers as nanosensing interface for vapor detection, at room temperature. The structural properties and surface morphology of the nanocomposite have been examined by X-ray diffraction, transmission and scanning electron microscopy, respectively. The sensing properties of SWCNTs nanocomposite LB films consisting of tangled nanotubules have been also investigated by using Quartz Crystal Microbalance 10 MHz AT-cut quartz resonators. The measured acoustic sensing characteristics indicate that the room-temperature SAW sensitivity to polar and nonpolar tested organic molecules (ethanol, ethylacetate, toluene) of the SWCNTs-in-CdA nanocomposite increases with the filler content of SWCNTs incorporated in the nanocomposite; also the SWCNTs-in-CdA nanocomposite vapor sensitivity results significantly enhanced with respect to traditional organic molecular cavities materials with a linearity in the frequency change response for a given nanocomposite weight composition and a very low sub-ppm limit of detection.

Investigations by X-ray topography of quartz and langasite resonators

This paper presents the results of the X-ray topography investigations of mass-loading influence on electrical parameters of AT-cut quartz resonators and Y-cut langasite resonators. This study reveals that the mass-loading effect on electrical parameters of Y-cut langasite resonators is smaller than in the case of AT-cut quartz resonators. The results of the X-ray topography investigations are in good agreement with electrical measurements.

Characteristics of Liquor Fragrance Detection by an AT-cut Quartz Resonator Having a Lecithin or Squalene Film

Characteristics of Liquor Fragrance Detection by an AT-cut Quartz Resonator Having a Lecithin or Squalene Film

QCM/HCC as a platform for detecting the binding of warfarin to an immobilized film of human serum albumin

Quartz crystal microbalance/heat conduction calorimetry (QCM/HCC) is a new measurement technology that has been used to monitor simultaneously the mass and motional resistance of a thin film in conjunction with the heat flow produced by a chemical change in the film initiated by reaction with a gas. In this work we examine the applicability of the QCM/HCC in detecting chemical changes at the solution/thin film interface. Human serum albumin (HSA) was bound to the gold electrode of a 5 MHz AT-cut quartz resonator using three types of linkers and then exposed to buffered solutions of the anticoagulant drug warfarin. Changes in resonator frequency and motional resistance as well as changes in heat flow produced by warfarin binding to HSA were monitored as a function of the warfarin concentration. Differences in frequency and motional resistance changes depend upon the linker and vary both in magnitude and sign, whereas the integrated heat signal is proportional to the concentration of warfarin and independent of the linker chemistry. Quartz crystal microbalance/heat conduction calorimetry can thus be a useful tool for studying protein-ligand interactions at the solution-surface interface, even though the quartz resonator does not behave as a microbalance.