E. Bigler

Stress-sensitivity mapping for surface acoustic waves on quartz

A model is presented, relating the velocity shifts of surface acoustic waves (SAW) to the six tensor components of quasistatic stresses. Stress sensitivity is then defined through six independent coefficients, whatever the origin of the stress (direct external forces, thermoelastic stresses) might be. These coefficients, depending on crystal anisotropy, are computed for different cut angles and propagation directions of quartz crystal, and represented as a contour-line mapping. The determination of SAW quartz cuts compensated for both planar isotropic stresses and first-order temperature effects make it possible to define a family of quartz cuts with potentially low stress and temperature sensitivities for oscillator applications.<<ETX>>

Lagrangian effective material constants for the modeling of thermal behavior of acoustic waves in piezoelectric crystals. II. Applications and numerical values for quartz

This paper presents a set of numerical values of temperature derivatives of Lagrangian effective elastic coefficients suitable for the modeling of small vibrations in quartz devices submitted to slow and homogeneous temperature variations. After a short description of the proper writing of vibration problems in practical applications with the help of this kind of coefficient, we determine the proposed set of numerical values from the frequency-temperature characteristics of an heterogeneous set of bulk and surface acoustic wave devices.

Precise modeling of complex SAW structures using a perturbation method hybridized with a finite element analysis

Surface acoustic wave (SAW) devices used in high stability oscillators or filters are generally designed to exhibit a low sensitivity to thermal and mechanical perturbations. Theoretical developments based on variational equations have been proposed to model these phenomena. Mechanical perturbations applied to simple geometries of the propagation substrate can be analytically considered using this approach. However, because of the strong dependence of mechanical effects on the geometry of the substrate, analytical models cannot provide realistic predictions on complex SAW structures subject to external stresses, vibrations, or accelerations. In this paper, an adaptation of the Tiersten-Sinha perturbation method is proposed, which combines the finite element analysis (for a precise prediction of quasi-static perturbations) and analytical variational equations of SAW propagation. Comparison of results obtained using simple analytical model and the proposed approach shows a very good agreement in the case of symmetrical radial in-plane compression on circular plates and monoaxial bending moments applied on rectangular substrates. This validation enables the consideration of more complicated configurations and allows using special stress-compensated SAW quartz cuts.

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 /spl mu/m, 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.

Experimental study of temperature effects in vibrating beam and thickness-shear resonators of GaPO/sub 4/ machined by ultrasonic milling

We report progress in modeling and measuring temperature effects in vibrating beam gallium orthophosphate (GaPO/sub 4/) resonators. In addition to the well known thickness-shear AT-cut, temperature compensated cuts exist in GaPO/sub 4/ for length extensional, flexural and torsional modes. Analytical models of temperature effects are compared with experimental measurements on devices fabricated on AT (Y-16.1/spl deg/) and Z-cut plates by ultrasonic machining. The agreement between theory and experiment is fairly good taking into account that temperature coefficients of GaPO/sub 4/ have been experimentally tested for only a few thickness-shear resonators.

High‐frequency surface acoustic wave devices at very low temperature: Application to loss mechanisms evaluation

Previous work on high‐performance bulk wave resonators in the frequency range of 5 to 25 MHz has shown that, by cooling to liquid helium temperature, acoustic losses become negligible. Therefore other sources of losses can be precisely measured. A similar approach is followed in the present work for high‐frequency surface wave resonators. Experiments have been performed at 416 MHz on quartz devices. It is shown that for surface waves propagating in a good surface acoustic wave (SAW) resonator an important source of acoustic loss is due to intrinsic acoustic losses. By cooling the device to below 30 K, the quality factor Q shows a T−4 dependence characteristic of intrinsic acoustic losses. Below 4–10 K a plateau region is reached. High Q values in the range of 1.5×105 have been obtained at 4.2 K for 416‐MHz devices, yielding a Q×f product of 7.5×1013 almost as good as for cooled bulk devices. Another set of measurements on a lithium niobate (LiNbO3) resonator at 847 MHz does not give a significant increase...

New results for the characterization of SAW sensitivity to mechanical stresses using finite element analysis

The anisotropy of quartz crystal is used in surface acoustic wave (SAW) devices to compensate for the influence of external perturbations (temperature or mechanical stress effects). Experimental results on the sensitivity of SAW quartz cuts to dynamical thermoelastic effects and to mechanical stress effects are studied in planar stress-compensated SAW quartz cuts. Theoretical predictions on the sensitivity to mechanical stresses (diametrical compression) are obtained either by analytical methods or by finite element analysis coupled to a perturbation method.<<ETX>>

Design and test of 3 GHz, fundamental mode STW resonators on quartz

Surface transverse wave (STW) resonators, based on the propagation of high velocity shear horizontal waves on Y-rotated quartz are 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, 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 /spl mu/m, operating frequency of 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) have been tested. Best results obtained at 3 GHz are: unloaded Q-factor Qu=2420, insertion loss I.L.=-10.3 dB (type 1) and Qu=1920, I.L.=-9.5 dB (type 2). The best experimental factor of merit Qu/spl times/f=7.5/spl times/10/sup 12/ is close to the best results already published for quartz STW resonators.

A perturbation method for modelling the thermal sensitivity of surface transverse wave (STW) propagation on a piezoelectric substrate

A perturbation method has been developed in order to correctly predict the sensitivity of surface transverse waves (STW) to quasi-static temperature effects. This approach is based on the coupling of unperturbed STW characteristics and thermoelastic properties of the substrate. The unperturbed STW parameters are calculated taking piezoelectricity into account for propagation under shallow grooves and thin metal strips. An analytical expression of the first order temperature coefficient is obtained in the case of grooves. Finite element analysis has been used for the case of metal strips deposited on crystalline substrate submitted to slow temperature variations. The validity of the results presented is carefully analysed and comparisons with available experimental data are discussed.<<ETX>>

Single and double side grating devices built on thin quartz plates for the excitation of surface transverse waves

A theoretical study of Surface Transverse Waves (STW) properties propagating on piezoelectric plates of finite thickness is proposed. Both cases of single and double side grating are considered in the model. The mechanical and electrical boundary conditions are described and the validity of the assumption used for the model is discussed in regard with experimental results. These results have been obtained for 140 /spl mu/m thick Z-cut plates and for 128 pm thick AT-cut plates with single-side aluminum strip gratings. Different delay lines have been fabricated. A relation between the theoretical dispersion curves exhibiting the existence of multiple frequency stopbands and the experimental frequency responses is emphasized. Also the frequency-temperature behaviour of a delay line built on a Z-cut plate has been measured.