Scattering matrix approach to STW resonators

The scattering matrix method was used for the analysis of surface transverse wave (STW) resonators on quartz. An expression for the transfer function of the resonators with different numbers of electrodes in the reflectors was derived. It was found that, for a proper ratio of these numbers, the spurious signal level below the resonance frequency can be lowered. The STW resonator for the frequency near 1090 MHz was designed, fabricated, and measured. By matching the measured and calculated transfer functions, the velocity, the electromechanical coupling coefficient, and the reflection coefficient of one aluminium strip of the STW on the 36°Y-cut quartz were determined. The insertion loss about 7 dB, loaded quality coefficient near 4200, and the spurious signal level about 5 dB lower compared with the resonance one were obtained for the resonator     

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.     

STW in-line acoustically coupled resonator filter on quartz

The scattering-matrix method was used for design of a surface transverse wave (STW) in-line acoustically coupled resonator filter on quartz. In this filter, two one-port STW resonators were coupled by means of a center reflector, grating phase shifters were placed between interdigital transducers and reflectors, and the pass band of the filter was located near the center frequency of the reflectors. At a frequency of about 509 MHz, insertion loss of about 5 dB and a 3 dB bandwidth of about 0.23 MHz was obtained. Differences between the measured and calculated amplitude responses are explained and design guidelines are presented. High STW velocity, low insertion loss, and very weak transverse mode make this filter attractive for high-frequency applications.     

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.     

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.     

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     

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.     

A coupling-of-modes approach to the analysis of STW devices

The dispersion characteristics of surface transverse waves (STW) on 36° rotated Y-cut quartz have been analyzed numerically. A closed form dispersion relation has been derived and introduced in the equations of the coupling-of-modes (COM) theory to account for the variation of energy trapping with frequency. The transmission and reflection coefficients at the finger edges have been determined from the stopband characteristics. Through the introduction of an electromechanical coupling which varies linearly with the electrode mass loading, quantitative agreement with experimental results on two different types of two-port STW resonators has been achieved, and characteristic features have been explained     

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.     

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.     

Flicker noise measurement of HF quartz resonators

Frequency flicker of quartz resonators can be derived from the measurement of S(phi) (f), i.e., the power spectrum density of phase fluctuations phi. The interferometric method appears to be the best choice to measure the phase fluctuations of the quartz resonators because of its high sensitivity in the low power conditions, which is required for this type of resonator. Combining these two ideas, we built an instrument suitable to measure the frequency flicker floor of the quartz resonators, and we measured the stability of some 10-MHB high performance resonators as a function of the dissipated power. The stability limit of our instrument, described in terms of Allan deviation sigma(y)(tau), is of some 10(-14).     

1/f noise in etched groove surface acoustic wave (SAW) resonators

Measurements of 1/f (or flicker) frequency fluctuations in SAW resonators fabricated with etched groove reflectors on single crystal quartz have shown that the observed noise levels vary inversely with device size. These measurements were made on sixteen 450 MHz resonators of four different sizes. The 1/f noise levels were also evaluated on twenty-eight other SAW resonators ranging in frequency from 401 to 915 MHz. This additional data provides valuable information on the dependence of the flicker noise levels on resonator frequency. A model based an localized, independent velocity fluctuations in the quartz is proposed which correctly fits the observed size and frequency dependence of the measured 1/f noise levels. This model suggests that the velocity fluctuations originate in small regions (much less than ~5 mum in diameter) randomly distributed throughout the quartz with an average separation of about 5 mum between independent (incoherent) sources. The magnitude of the localized fractional velocity fluctuations, Deltav/v, averaged over a 5 micron cube is on the order of 1x10 (-9).     

Monolithic miniaturized quartz microbalance array and its application to chemical sensor systems for liquids

We report on the design, fabrication, and application of novel monolithic miniaturized quartz microbalance (QMB) arrays. Up until now, almost all reported resonator arrays (often designated as "electronic noses" or "electronic tongues", respectively, dependent on their application) are assembled from single QMBs. We fabricate arrays with up to 36 QMBs on a single AT-cut quartz blank. Mass sensitive devices based on AT-cut quartz resonators are suitable as (bio)chemical sensors. A frequency shift caused by mass accumulation on the sensor surface increases theoretically with f/sup 2/, hence the detection limits for the application as chemical sensors should be decreased with increasing frequency. Since the quality factor Q of a quartz crystal decreases with f, the frequency stability is reduced, thus limiting mass sensitivity. The mass sensitivity of resonators with different resonant frequencies was examined by means of electrochemical copper deposition on their surface. Subsequently, the manufactured resonators were coated with different layers (polystyrene, amyl-calix[8]arene, /spl beta/-cyclodextrine). In order to examine the applicability of such coatings as sensitive layers, their sensitivities to toluene in water were investigated. Moreover, arrays with up to four different resonant frequencies on one chip were fabricated for comparing the resonator behavior of the same coating at different frequencies. In another test setup, different layers were sprayed onto an array of microbalances having all the same resonant frequency. This allowed for comparing the different coating behavior under equivalent test conditions. Arrays were tested for viscosity measurement to find an optimum resonant frequency.     

Surface transverse waves exceed the material Q limit for surfaceacoustic waves on quartz

State-of-the-art 1.244-GHz surface transverse wave (STW) resonators on AT-cut quartz are characterized. They demonstrate an unloaded Q of 8144 which is as high as 97% of the material Q limit for surface acoustic waves (SAWs). By analyzing the measured data and accounting for the ohmic loss, it is shown that the material Q for STWs on quartz, experimentally obtained from these devices, is at least 37% higher than the material Q for SAWs     

Characterization of sol-gel Pb(Zr0.53Ti0.47O3) in thin film bulk acoustic resonators

The behavior of {f111g}-textured Pb(Zr(0.53Ti0.47O3) (PZT) deposited by the sol-gel technique in thin film bulk acoustic resonators (TFBAR's) was investigated at a resonance frequency of about 1 GHz. The resonators were fabricated on Si wafers using deep silicon etching to create a membrane structure and using platinum as top and bottom electrodes. The best response of the resonators was observed at a bias voltage of -15 kV/cm with values of about 10% for the coupling constant and about 50 for the quality factor. This voltage corresponds to optimal values of piezoelectric constant d33 and dielectric constant measured as a function of the electric field. The influence of a bias voltage on the resonance frequency, antiresonance frequency, and coupling constant were observed. Both the resonance and antiresonance frequency show a hysteretic change with applied bias. This effect can be used to shift the whole band of a filter by applying a voltage. The TFBAR structure also allowed us to extract values for materials parameters of the PZT film. Dielectric, piezoelectric, and elastic properties of the f111g-textured PZT film are reported and compared to direct measurements and to literature values.     

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.     

Multichannel quartz crystal microbalance

Arrays of quartz crystal resonators are fabricated on a single quartz wafer as a multichannel quartz crystal microbalance (MQCM). Three types of four-channel array of 10-MHz resonators are prepared and tested. Mechanical oscillation of each channel is entrapped within the channel almost completely, so that the interference between the channels via the quartz crystal plate is almost negligible. A mass change on each channel is quantitatively evaluated on the basis of Sauerbrey's law. Thus, each channel of a MQCM device can be used as an independent QCM. Influence from a longitudinal wave generated from another channel is also negligible compared to the influence from the wave from the monitored channel itself. The simultaneous oscillation of channels is also possible. The potential applicability of MQCM to the two-dimensional mapping of mass changes is demonstrated.     

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).     

A Frequency-Lock System for Improved Quartz Crystal Oscillator Performance

The intrinsic noise of the best quartz crystal resonators is significantly less than the noise observed in oscillators employing these resonators Several problem areas common to traditional designs are pointed out and a new approach is suggested for their solution. Two circuits are described which frequency lock a spectrally pure quartz crystal oscillator to an independent quartz crystal resonator. The performance of the composite system is predicted based on the measured performance of its components.     

Acceleration sensitivity of surface wave resonators

In light of the substantial performance advantages of STW over SAW in various areas, theoretical and experimental studies of the acceleration sensitivities of STW and SAW resonators have been undertaken. The purpose of the studios has been to understand the fundamental nature of STW and SAW acceleration sensitivities, and to determine whether the performance advantages of STW seen in other areas extend to the case of acceleration sensitivity. The basic approach utilizes the perturbation theory developed by Tiersten to calculate the acceleration sensitivities of both STW and SAW resonators. The acceleration-induced bias is conveniently written in terms of acceleration-induced deformation gradients and factored elastic stiffness expressions. This representation clarifies important concepts regarding the frequency shift and the involved elastic constants, and provides the designer with insight into the basic nature of the problem. The dependencies of the normal acceleration sensitivities on substrate and mode shape parameters and the fundamental nature of plate flexure are discussed at length. The calculations compare favorably to recent experimental results