Theory and design of piezoelectric resonators immune to acceleration: present state of the art

A typical low noise oscillator uses a crystal resonator as the frequency-determining element. An understanding of the fundamental nature of acceleration sensitivity in crystal oscillators resides primarily in understanding the behavior of the crystal resonator. The driving factor behind the acceleration-induced frequency shift is shown to be deformation of the resonator. The deformation drives two effects: an essentially linear change in the frequency-determining dimensions of the resonator and an essentially nonlinear effect of changing the velocity of the propagating wave. In this paper, the fundamental nature of acceleration sensitivity is reviewed and clarified, and attendant design guidance is developed for piezoelectric resonators. The basic properties of acceleration sensitivity and general design guidance are developed through the simple examples of “bulk acoustic wave (BAW) in a box” and “surface transverse wave (STW) in a box.” These examples serve to clarify a number of concepts, including the role of mode shape and the basic difference between the BAW and STW cases. The design equations clarify the functional dependencies of the acceleration sensitivities on the full range of crystal resonator design and fabrication parameters     

Coupling-of-modes analysis of STW resonators including loss mechanism

Surface transverse wave (STW) resonators exhibit substantial advantages over conventional surface acoustic wave (SAW) resonators. However, their analysis is more involved because of the complicated nature of STW. Many parameters have been studied, but the one that has been difficult to analyze accurately is the quality factor Q, which is of great importance for characterizing the devices. At present, none of the available analytical models is concerned with quantitative loss consideration, and the establishment of reliable design rules is difficult. We present a theoretical study that allows one to conduct coupling-of-modes (COM) STW loss analysis and estimate the resonator Q from material and layout parameters. The COM transmission coefficient χ₁₁ is derived by Floquet analysis. Its imaginary part is obtained by numerically fitting available experimental data for the Q-factor of particular resonators. It is a measure of STW propagation loss that adds to the electrode reflection loss     

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.     

Gigahertz range resonant devices for oscillator applications using shear horizontal acoustic waves

It is shown that surface transverse wave (STW) resonant devices are not only very well suited for stable oscillator applications but have some unique features offering greater design flexibility than their surface acoustic wave (SAW) counterparts. Various designs for single- and multimode resonators and resonator filters are presented, and their properties in respect to applications in stable fundamental-mode fixed-frequency and voltage-controlled oscillators in the range of 750 MHz to 2 GHz are discussed. Characteristics of SAW and STW two-port metal strip resonators using identical designs are compared. Data from frequency trimming on STW resonators, using heavy ion bombardment, are presented.     

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.     

Gas sensitivity comparison of polymer coated SAW and STW resonators operating at the same acoustic wave length

Results from systematic gas sensing experiments on polymer coated surface-transverse-wave (STW) and surface-acoustic-wave (SAW) based two-port resonators on rotated Y-cut quartz, operating at the same acoustic wavelength of 7.22 /spl mu/m, are presented. The acoustic devices are coated with chemosensitive films of different viscoelastic properties and thicknesses, such as solid hexamethyldisiloxane (HMDSO), semisolid styrene (ST), and soft allyl alcohol (AA). The sensor sensitivities to vapors of different chemical analytes are automatically measured in a sensor head, evaluated, and compared. It is shown that thin HMDSO- and ST-coated STW sensors are up to 3.8 times more sensitive than their SAW counterparts, while SAW devices coated with thick soft AA-films are up to 3.6 times more sensitive than the STW ones. This implies that SAWs are more suitable for operation with soft coatings while STWs perform better with solid and semisolid films. A close-to-carrier phase noise evaluation shows that the vapor flow homogeneity, the analyte concentration, its sorption dynamics, and the sensor oscillator design are the major limiting factors for the sensor noise and its resolution. A well designed ST-coated 700 MHz STW sensor provides a 178 kHz sensor signal at a 630 ppm concentration of tetra-chloroethylene and demonstrates short-term stability of 3/spl times/10/sup -9//s which results in a sensor resolution of about 7 parts per billion (ppb).     

Accurate measurement of anhydride fluorhydric acid concentration in controlled gaseous flow with STW sensors

This paper presents theoretical and experimental developments for the implementation of surface acoustic waves (SAW) sensors able to detect small concentrations of anhydride fluorhydric (HF) acid in air. Solutions based on the use of surface transverse waves (STW) on quartz (YXlt)/36 degrees/90 degrees have been analyzed to evaluate their sensitivity to HF. Devices have been tested first in a NH4F solution to evaluate the kinetics of the reaction. Measurements then were performed under various gaseous conditions to characterize the sensors when they are submitted to different controlled dilutions of HF in air. STW resonators have been successfully tested in different conditions, with capabilities to detect HF concentration much smaller than 1 ppm.     

Design and test of 3 GHz, fundamental mode surface transverse wave resonators on quartz

Surface transverse wave (STW) resonators, based on the propagation of high velocity shear horizontal waves on Y-rotated quartz were designed, fabricated and tested. A model is presented to predict the resonant frequency of a 3-grating structure as a function of design parameters such as periodicities, metal thickness, and finger-to-gap ratio. Experimental devices have been fabricated by direct e-beam lithography with linewidth geometries in the range of 0.3-0.5 mum, and an operating frequency close to 3 GHz in fundamental mode. Two different designs using either a quasi synchronous structure (type 1) or a change of periodicity inside the cavity (type 2) were tested. The best experimental factor of merit is close to the best results already published for quartz STW resonators.     

The coupling-of-modes approach to the analysis of STW devices. II

For pt. I see ibid., vol. 44, no. 3, p. 652-7 (1997). The method for analyzing surface transverse wave (STW) devices by using a coupling-of-modes (COM) formalism has been completed, covering the STW electromechanical coupling coefficient (ECC). An ECC analytical formula has been derived by fitting numerical results from STW effective permittivity analysis. The ECC exhibits frequency and mass-loading variation. Using this new result, a satisfactory agreement with available experimental frequency characteristics of STW two-port quartz resonators has been achieved, without the necessity of additional experimental information. In its present form, the method is self-consistent and applicable to arbitrary STW layouts.     

High Q metal strip SSBW resonators using a SAW design

An experimental study of metal strip surface skimming bulk wave (SSBW) resonators using a surface acoustic wave (SAW) design is presented. Characteristics of SSBW and SAW resonators fabricated with the same photolithographic mask are compared and discussed. High Q low-loss SSBW resonators are achieved using a conventional two-port SAW resonator design and taking special care of the distance L between both interdigital transducers, the metal thickness h/lambda (lambda=acoustic wavelength) and the finger-to-gap ratio. Best overall performance of the SSBW devices in this study is achieved at L=nlambda/2-lambda/4 (compared with L=nlambda/2-lambda/8 for SAW resonators), h /lambda=1.6% (compared with 2% for SAW), and finger-to-gap ratio close to 1. The best device fabricated shows an unloaded Q of 5820 and an insertion loss of 7.8 dB at 766 MHz. The SSBW resonant frequency shows a stronger dependence on the metal thickness than the SAW one. This problem, however, is readily solved by frequency trimming using a CF(4) plasma etching technique. SSBW resonator can be trimmed by 0.2% down in frequency (compared with 0.05% for SAW) without affecting their performance.     

Design of SAW synchronous resonators on ST cut quartz

Surface acoustic wave (SAW) resonators on ST cut quartz, with synchronous placement of the interdigital transducers (IDT), were designed, fabricated, and measured. The basic structure of the resonators was a two-port one. The one-port resonators were obtained by parallel connection of the two IDT or by short circuiting one of them. The IDT were apodized to eliminate coupling to spurious modes. The transfer function of the two-port resonators was calculated by using the scattering matrix method. Several models of these resonators were investigated in the frequency range from about 300 to 715 MHz. By matching the theoretical and experimental transfer functions, the loss coefficient as a function of frequency and the SAW velocity in the reflector area as a function of aluminium layer thickness were determined. The responses of the resonators were free of any spurious modes.     

Prediction of the thermal sensitivity of surface acoustic waves excited under a periodic grating of electrodes

The prediction of the temperature sensitivity of surface acoustic wave (SAW) devices still requires improvement because the nature of the implemented surface modes and the devices' complexity strongly change from the early basic Rayleigh-wave-based devices. To address this problem, a theoretical analysis and a numerical tool have been developed to predict the thermal dispersion of general electro-acoustic devices. The proposed model accounts for the electrode contribution to the frequency-temperature law. The computed thermal sensitivities are compared to experimental results for different kinds of substrates and waves.     

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     

Suppression of Transverse Mode Responses in Ultra-Wideband SAW Resonators Fabricated on a Cu-Grating/15°YX-LiNbO 3 Structure

This paper discusses a technique to suppress spurious transverse mode responses appearing in ultra-wideband SAW resonators fabricated on a Cu- grating/15degYX-LiNbO₃ structure. The basic idea of the technique is inserting length- and width-weighted dummy electrodes between a bus-bar and interdigital electrodes. For practical device design, an analysis was made to show how the profile (field distribution) of both dominant and spurious transverse modes depends on the length and width (equivalent to SAW velocity) of the dummy electrodes. IDT-type SAW resonators were fabricated on a Cu- grating/15degYX-LiNbO₃ structure using the length- and width-weighted dummy electrodes. The experimental results were in good agreement with the theoretical analysis and prediction, showing that the proposed technique is effective in suppressing the spurious responses caused by the transverse modes.     

Suppression of transverse mode responses in ultra-wideband SAW resonators fabricated on a Cu-grating/15 degrees YX-linbO3 structure.

This paper discusses a technique to suppress spurious transverse mode responses appearing in ultra-wideband SAW resonators fabricated on a Cu-grating/15 degrees YX-LiNbO3 structure. The basic idea of the technique is inserting length- and width-weighted dummy electrodes between a bus-bar and interdigital electrodes. For practical device design, an analysis was made to show how the profile (field distribution) of both dominant and spurious transverse modes depends on the length and width (equivalent to SAW velocity) of the dummy electrodes. IDT-type SAW resonators were fabricated on a Cu-grating/15 degrees YX-LiNbO3 structure using the length- and width-weighted dummy electrodes. The experimental results were in good agreement with the theoretical analysis and prediction, showing that the proposed technique is effective in suppressing the spurious responses caused by the transverse modes.     

Surface transverse waves: properties, devices, and analysis

Surface transverse waves represent a new generation of the surface acoustic wave (SAW) family that offers advantageous properties without further demand for new materials or improved design and technology. The most effective activity in the surface transverse wave (STW) area has been realized during the last decade with high-performance devices achieved and analytical methods developed. The present paper reviews the basic achievements in historical and factual order. A state-of-the-art introduction is combined with discussion on the development tendencies with specific emphasis on sensor technology.     

Polymer coating behavior of Rayleigh-SAW resonators with gold electrode structure for gas sensor applications

Results from systematic polymer coating experiments on surface acoustic wave (SAW) resonators and coupled resonator filters (CRF) on ST-cut quartz with a corrosion-proof electrode structure entirely made of gold (Au) are presented and compared with data from similar SAW devices using aluminium (Al) electrodes. The recently developed Au devices are intended to replace their earlier Al counterparts in sensor systems operating in highly reactive chemical gas environments. Solid parylene C and soft poly[chlorotrifluoroethylene-co-vinylidene fluoride] (PCFV) polymer films are deposited under identical conditions onto the surface of Al and Au devices. The electrical performance of the Parylene C coated devices is monitored online during film deposition. The PCVF coated devices are evaluated after film deposition. The experimental data show that the Au devices can stand up to 40% thicker solid films for the same amount of loss increase than the Al devices and retain better resonance and phase characteristics. The frequency sensitivities of Au and Al devices to parylene C deposition are nearly identical. After coating with soft PCFV sensing film, the Au devices provide up to two times higher gas sensitivity when probed with cooling agent, octane, or tetrachloroethylene.     

Extremely low-phase-noise SAW resonators and oscillators: design and performance

The authors describe prototype low-noise SAW (surface acoustic wave) resonator oscillators which have demonstrated state-of-the-art phase-noise performance not only at their fundamental operating frequencies in the 400- to 600-MHz range but also after 16x frequency multiplication to X-band as well. SAW resonator designs with overmoded cavities, very wide apertures, and dual apertures, as well as modified fabrication techniques, have been used to realize an overall reduction in an oscillator's phase-noise spectrum, i.e. white phiM, flicker FM, and random-walk FM. The S resonators can typically handle incident RF power in excess of +20 dBm, a key requirement to achieving an extremely low oscillator-phase-noise floor. A novel burn-in procedure at relatively high incident-RF-power levels (>27 dBm) was used to reduce both the flicker FM and random-walk FM phase-noise levels. Using these various techniques, a 5- to 15-dB improvement in the overall phase-noise spectrum for several prototype oscillators was demonstrated.     

Redeposition: a factor in ion-beam etching topography

The design of high performance SAW resonators and reflection pulse compression filters using grooves as the reflective arrays requires that the profiles of the grooves be rectangular and reproducible. The use of neutralized ion-beam technology has largely been adopted for etching these grooves in quartz and lithium niobate because of the precision and control which can be exercised in its use. The experimental work presented here asserts the major contribution that redeposition makes in the evolution of ion-beam etched topography of amorphous, polycrystalline and crystalline materials in a way which is directly useful to the determination of groove profiles. Data are also presented on the relationship between the incidence angle of the ion beam and the etch rate of some important SAW materials indicating the connection between this function and the etching characteristics of the materials.