Precision frequency trimming of SAW and STW resonators using Xe(+) heavy ion bombardment

A method for precision frequency trimming of surface acoustic wave (SAW) and surface transverse wave (STW) based resonant devices using a Xe(+) heavy ion bombardment technique is described. The devices are downtrimmed in frequency in an in-situ monitoring process by means of a Kaufmann type ion source that allows first a rough and then a fine frequency trimming with an accuracy of 1 ppm in a single continuous in-situ monitoring process. An improvement of the device insertion loss and unloaded Q as a result of the trimming process is achieved. Single mode 776 MHz STW resonators can be downtrimmed by more than 5000 ppm without deteriorating their parameters while SAW resonators allow a much lower frequency downshift. The method is simple and can cost effectively be applied to SAW and STW device fabrication.     

Calculation and experimental verification of the acoustic stress at GHZ frequencies in SAW resonators

High power applications of Surface Acoustic Wave (SAW) devices may lead to acoustomigration in their thin metal electrodes, which deteriorates the performance or may even destroy the SAW device. It is confirmed in this paper that the mechanism of acoustomigration is caused by the SAW-induced stress in the metal. The quantitative calculation of this stress will be shown in detail, starting from the widely used P-Matrix model as a standard analysis tool. The combination with the partial wave method (PWM) yields the stress distribution inside the metal. This approach provides the flexibility to determine the stresses for any given point in a SAW device, for any input power, frequency, wavetype, device geometry, or metal layer. In order to confirm the absolute values of the stress components, we calculated and measured displacements as a function of input power and frequency.     

Theoretical and experimental mass-sensitivity analysis of polymer-coated SAW and STW resonators for gas sensing applications

Polymer-coated surface transverse waves (STW) resonators have recently been successfully studied for organic gas sensing applications. The first results indicate increased absolute and even relative sensitivity as compared to similar resonators with surface acoustic waves (SAW). However, the gain in sensitivity is accompanied by the adverse effect of an increased attenuation and the advantage frame is difficult to establish quantitatively. In this paper, a new set of experimental samples with Parylene C-coated quartz substrates are studied. The samples are matched in frequency and wavelength. The results are compared and the obtained features explained using available theoretical algorithms for analyzing layered SAW and Love configurations, and a recently developed STW algorithm. The approximate limits of advantageous applicability of the STW resonator gas sensors are discussed.     

Dispersion and mirror transmission characteristics of bulk acoustic wave resonators

A heterodyne laser interferometer is used for a detailed study of the acoustic wave fields excited in a 932-MHz solidly mounted ZnO thin-film BAW resonator. The sample is manufactured on a glass substrate, which also allows direct measurement of the vibration fields from the bottom of the acoustic mirror. Vibration fields are measured both on top of the resonator and at the mirror-substrate interface in a frequency range of 350 to 1200 MHz. Plate wave dispersion diagrams are calculated from the experimental data in both cases and the transmission characteristics of the acoustic mirror are determined as a function of both frequency and lateral wave number. The experimental data are compared with 1-D and 2-D simulations to evaluate the validity of the modeling tools commonly used in mirror design. All the major features observed in the 1-D model are identified in the measured dispersion diagrams, and the mirror transmission characteristics predicted for the longitudinal waves, by both the 1-D and the 2-D models, match the measured values well.     

Fabrication and performance analysis of film bulk acoustic wave resonators

In this paper, a radio frequency reactive sputtering deposition technique for piezoelectric aluminum nitride (AlN) thin film formation on a gold (Au) bottom electrode and its successful application in a film bulk acoustic resonator (FBAR) are investigated. The X-ray diffraction (XRD), scanning electron microscopy (SEM), and atomic force microscopy (AFM) measurements show that the AlN films were deposited onto an Au bottom electrode with highly c-axis-preferred orientation, well-textured columnar structure with a fairly uniform grain size of approximately 83 nm. The roughness is measured at a root-mean square (RMS) value of 5.4 nm and the average peak to valley of each grain column is 46.3 nm. The FBAR consists of an AlN piezoelectric thin film sandwiched between Au electrodes, all of which lie on a thin low-stress silicon nitride which serves as a support membrane on silicon. The performance of FBAR device exhibits a significant of the series quality factor (Q_s), the parallel quality factor (Q_p), the effective electromechanical coupling coefficient (k_eff²), and the bandwidths are 97, 120, 5.1%, and 24 MHz, respectively.     

Mass sensitivity calculation of the protein layer using love wave SAW biosensor

Love waves, a variety of surface acoustic waves (SAWs), can be used to detect very small biological surface interactions and so have a wide range of potential applications. To demonstrate the practicality of a Love wave SAW biosensor, we fabricated a 155-MHz Love wave SAW biosensor and compared it with a commercial surface Plasmon resonance (SPR) using glycerol-water solution with known densities and viscosities to calibrate the response signals of the biosensors. And the mass per unit area of anti-mouse IgG bound with protein G onto the sensitive layer of the biosensor was calculated on the basis of the calibration result. The sensitivity of the Love wave SAW biosensor was the same as or greater than that of the SPR biosensor. Furthermore, the Love wave SAW biosensor was capable of measuring a much wider range of viscosities than the SPR biosensor. Although the operating principle of the Love wave SAW biosensor is completely different from that of the SPR biosensor, the subtle changes in the viscoelastic properties of the biological layer that accompany biological binding reactions on the sensitive layer can be monitored and measured in the same ways as with the SPR biosensor.     

Coupling-of-modes analysis and modeling of polymer-coated surface acoustic wave resonators for chemical sensors

The analysis and modeling of SAW resonator devices based on the coupling-of-modes (COM) theory are described, integrating the effect of polymer coating so that the sensor effects can be accounted for in the device transfer function. Based on the perturbation method, the effects of film coating are included in determining the parameters for the model. The COM parameters are, therefore, modified and its simple analytical approaches are presented. The model is validated using the experimental data of a two-port SAW resonator device fabricated on ST-X quartz substrate. The experimental results for a device coated with Parylene C are compared with the simulation results of the proposed model. The comparative results of the electrical characteristics and the frequency sensitivity to film thickness show a good agreement which proves the validity of the model. This analysis and model will provide insight into the influence of the device design parameters on the sensor performance and help in practical design and optimization of SAW-based chemical sensor systems.     

Frequency-dependent open-circuit acoustic sensitivity of fluid-filled, coated, radially polarized piezoelectric ceramic cylindrical shells of arbitrary thickness and infinite length

The frequency-dependent free-field open-circuit voltage generated by radially polarized piezoelectric ceramic fluid-filled shells of infinite length coated with an elastic layer and excited by a plane acoustic wave is studied. The shell and the coating are of arbitrary thickness and are anisotropic. It is shown that the charge density in the piezoelectric shell is zero by using the electrostatic and open-circuit conditions. General expressions for the pressures and radial velocities in the interior and exterior fluids are obtained by using the finiteness and radiation conditions, respectively. General expressions for the radial stresses and velocities in the piezoelectric shell and elastic coating are also determined by using two-dimensional equations of state and axisymmetric equations of motion. The coefficients in the general expressions are then determined by using the continuity conditions at the various interfaces. Finally, an expression for the open-circuit sensitivity is obtained by using a piezoelectric equation of state. Numerical results are presented for air, water, and vacuum in the interior, two types of elastic coating, and piezoelectric shells with various thicknesses. The effect of neglecting anisotropy on the sensitivity is also illustrated     

Investigation of the scaling rules determining the performance of film bulk acoustic resonators operating as mass sensors

Solidly mounted (SMR-type) thin film bulk acoustic resonators operating at 2.2, 4.1, and 8.0 GHz and with lateral extents from 30 to 500 microm were fabricated and their performance as mass sensors was evaluated theoretically as well as experimentally. It was found that increasing the frequency leads to a principally improved performance of these devices. Problems arising for the horizontal as well as the vertical dimension and structure are investigated.     

Synthesis and bulk acoustic wave properties on the dual mode frequency shift of solidly mounted resonators

This study focused on the fabrication and the theoretical analysis of solidly mounted resonators (SMR) concerning dual-mode frequency responses and their frequency shift of bulk acoustic wave (BAW) resonance. For this device fabrication, RF/DC magnetron sputtering and photolithography were employed to constitute the required multilayer structure. For the theoretical analysis, the dualmode frequency shift was characterized by the Sauerbrey's formula, and a modified formula was carried out following the trend for the large frequency shift. In the fabrication of the SMR device, Mo/SiO2 was chosen to construct the Bragg reflector as the high/low acoustic impedance materials, respectively, and aluminum nitride (AlN) was used as a piezoelectric layer. To investigate the characteristics of BAW on the dual-mode frequency shift, the c-axis tilted angle of AlN was altered as well as the various mass loading on the SMR. Based on the experimental results, the dual-resonance frequencies showed a nonlinear decreasing trend with a linear increase of the mass loading. Therefore, a modified formula was carried out. Furthermore, the ratio of the longitudinal-resonant frequency to the shear-resonant frequency remained at a range around 1.76 despite the various c-axis tilted angles of AlN and gradual mass loading on the SMR. The electromechanical coupling coefficient, k2(eff), of the shear resonance rose with the increase of the c-axis tilted angle of AlN.     

A micromachined vibration isolation system for reducing the vibration sensitivity of surface transverse wave resonators

A micromachined system has been developed for reducing the vibration sensitivity of surface transverse wave (STW) resonators. The isolation system consists of a support platform for mounting the STW resonator, four support arms, and a support rim. The entire isolation system measures 8 mm by 9 mm by 0.4 mm without the resonator mounted on the platform. The system acts as a passive vibration isolation system, decreasing the magnitude of high frequency (>1.2 kHz) vibrations. Finite element analysis is used to analyze the acceleration sensitivity of the mounted resonator. The isolation system is then modeled as a damped mass-spring system and the transmissibility of vibration from the support rim to the support platform is calculated. Multiplying the acceleration sensitivity of the resonator by the transmissibility results in the expected system vibration sensitivity. The isolation systems are fabricated using two sided bulk etching of (110) oriented silicon wafers. STW resonators were mounted on the isolation systems, and the isolated units were mounted on commercial hybrid oscillator substrates. Vibration sensitivity measurements were taken for vibrations with frequencies ranging from 100 Hz to 5 kHz. The measured data show that the system performs as expected with a low frequency (<500 Hz) vibration sensitivity of 1.8×10^-8/g and a high frequency roll off of 12 dB/octave     

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.     

Mass sensitivity of the thin-rod acoustic wave sensor operated in flexural and extensional modes

The mass sensitivities of the thin-rod acoustic wave sensor in both flexural and extensional acoustic modes are presented. These are based on experiments involving the electrodeposition of a test loading material onto a thin metal fiber (the thin rod) in a delay line configuration. Only small changes in acoustic loss occur when the device is immersed in an electrolyte, particularly in the flexural mode. Copper and lead have been used as test materials to confirm that the effects of elasticity can give rise to positive and negative mass sensitivities, respectively. The experimental and theoretical values all agree in sign and are of the same order of magnitude. This result confirms a refined theoretical model that includes incorporation of the effects of elasticity and inertia. An increase in experimental mass sensitivity with decrease in fiber radius is one of the advantages for the construction of a sensitive chemical sensor based on the thin-rod device. The sensor can be operated with facility in both gas and liquid phases and offers a new technique for the study of interfacial electrochemistry on metal surfaces. The phenomenon of mechanical resonance was observed during a number of experiments.     

The state of the art of flicker frequency noise in BAW and SAW quartz resonators

Experimental results of the last 15 years are reviewed. Noise properties of crystal filters and oscillators are reported, along with practical measurements. It is shown that the additional phase fluctuations are compensated by frequency fluctuations and vice versa. With the assistance of these theoretical results the flicker and white frequency noise coefficients, h(-1) and h(0), respectively, are plotted versus unloaded Q and carrier frequency f(0) for the measured and published crystal oscillator noise characteristics. The dependence of h(-1) approximately 10(-12.75) Q(2) (u) is verified.     

Ince-Gaussian modes of the paraxial wave equation and stable resonators

We present the Ince-Gaussian modes that constitute the third complete family of exact and orthogonal solutions of the paraxial wave equation in elliptic coordinates and that are transverse eigenmodes of stable resonators. The transverse shape of these modes is described by the Ince polynomials and is structurally stable under propagation. Ince-Gaussian modes constitute the exact and continuous transition modes between Laguerre- and Hermite-Gaussian modes. The expansions between the three families are derived and discussed. As with Laguerre-Gaussian modes, it is possible to construct helical Ince-Gaussian modes that exhibit rotating phase features whose intensity pattern is formed by elliptic rings and whose phase rotates elliptically.     

Quantitative acoustic microscopy of anodized and coated aluminium at frequencies up to 1 GHz

Quantitative acoustic microscopy (QAM) has been used to measure surface wave velocities on polished, anodized and coated aluminium substrates, these materials being representative of those used for adhesive bonding in the aerospace industry. Good quality acoustic measurements were obtainable at frequencies between 225 and 980 MHz, despite the inhomogeneous nature of the oxide layer produced by phosphoric acid anodization (PAA). Good agreement was obtained between the surface acoustic wave dispersion measured on aluminium coated with 0.2 and 1.0 m PMMA, and that calculated by a simple isotropic layer model. The anodized aluminium was modelled as a transversely isotropic oxide layer on an aluminium substrate. At 0.2 m, the oxide layer was too thin for the comparison between measurement and calculation to be conclusive, but the calculations suggest that a change in porosity of 10% in a 0.6 m oxide layer, as obtained with an industry standard PAA treatment, should be readily detectable. The highly dispersive nature of some of the surface acoustic wave modes makes QAM extremely sensitive to small changes in the material parameters.     

Applicability of LiNbO3, langasite and GaPO4 in high temperature SAW sensors operating at radio frequencies

The applicability of LiNbO3, langasite and GaPO4 for use as crystal substrates in high temperature surface acoustic wave (SAW) sensors operating at radio frequencies was investigated. Material properties were determined by the use of SAW test devices processed with conventional lithography. On GaPO4, predominantly surface defects limit the accessible frequencies to values of 1 GHz. Langasite SAW devices could be operated up to 3 GHz; however, high acoustic losses of 20 dB/micros were observed. On LiNbO3, the acoustic losses measured up to 3.5 GHz are one order of magnitude less. Hence, SAW sensors capable of wireless interrogation were designed and processed on YZ-cut LiNbO3. The devices could be successfully operated in the industrial-scientific-medical (ISM) band from 2.40 to 2.4835 GHz up to 400 degrees C.     

Effects of H2O partial pressure on the crystallinity of ZnO thin film and electrical characteristics of film bulk acoustic wave resonators

We have improved electrical characteristics of a film bulk acoustic wave (BAW) resonator that features the injection of H₂O gas into a process chamber. The preferred crystallinity of piezoelectric ZnO film was obtained by RF sputtering at a high H₂O partial pressure 1.5×10⁻⁴ Pa. The effective electromechanical coupling coefficient () of the BAW resonator remarkably goes up from 1.8% to 4.7% for which the corresponding H₂O partial pressures are 2.7×10⁻⁵ and 1.5×10⁻⁴ Pa. Injection of H₂O during the deposition process contributes to the improvement of crystallinity of ZnO thin film and the electrical characteristics of the BAW resonator.     

Acceleration sensitivity of crystal resonators affected by the mass and location of electrodes

Predominant thickness-shear frequencies and modes of a crystal plate with electrodes of arbitrary shape and mass distribution are obtained by a finite-element method, based on Mindlin's first-order equations with platings. These frequencies and modes are used in a perturbation method for computing the acceleration sensitivity of crystal resonators with electrodes. Computations are made for a square AT-cut quartz plate that is supported by a four-point mount and coated with identical square and uniform electrodes on the upper and lower faces of the plate. To study the effect of uneven distribution of electrode mass, acceleration sensitivities are calculated when a small mass is added at various locations near the edges of the square electrodes. It is found that the percent increase of the acceleration sensitivity of the resonator with a small added mass to that of the resonator without added mass ranges from 3.8% to 541.7%, depending on the location of the small mass placed at the edges of the electrodes.     

Comparisons of polymer/gas partition coefficients calculated from responses of thickness shear mode and surface acoustic wave vapor sensors

Apparent partition coefficients, K, for the sorption of toluene by four different polymer thin films on thickness shear mode (TSM) and surface acoustic wave (SAW) devices are compared. The polymers examined were poly(isobutylene) (PIB), poly(epichlorohydrin) (PECH), poly(butadiene) (PBD), and poly(dimethylsiloxane) (PDMS). Independent data on partition coefficients for toluene in these polymers were compiled for comparison, and TSM sensor measurements were made using both oscillator and impedance analysis methods. K values from SAW sensor measurements were about twice those calculated from TSM sensor measurements when the polymers were PIB and PECH, and they were also at least twice the values of the independent partition coefficient data, which is interpreted as indicating that the SAW sensor responds to polymer modulus changes as well as to mass changes. K values from SAW and TSM measurements were in agreement with each other and with independent data when the polymer was PBD. Similarly, K values from the PDMS-coated SAW sensor were not much larger than values from independent measurements. These results indicate that modulus effects were not contributing to the SAW sensor responses in the cases of PBD and PDMS. However, K values from the PDMS-coated TSM device were larger than the values from the SAW device or independent measurements, and the impedance analyzer results indicated that this sensor using our sample of PDMS at the applied thickness did not behave as a simple mass sensor. Differences in behavior among the test polymers on SAW devices are interpreted in terms of their differing viscoelastic properties.