E.L. Adler

Matrix methods applied to acoustic waves in multilayers

Matrix methods for analyzing the electroacoustic characteristics of anisotropic piezoelectric multilayers are described. The conceptual usefulness of the methods is demonstrated in a tutorial fashion by examples showing how formal statements of propagation, transduction, and boundary-value problems in complicated acoustic layered geometries such as those which occur in surface acoustic wave (SAW) devices, in multicomponent laminates, and in bulk-wave composite transducers are simplified. The formulation given reduces the electroacoustic equations to a set of first-order matrix differential equations, one for each layer, in the variables that must be continuous across interfaces. The solution to these equations is a transfer matrix that maps the variables from one layer face to the other. Interface boundary conditions for a planar multilayer are automatically satisfied by multiplying the individual transfer matrices in the appropriate order, thus reducing the problem to just having to impose boundary conditions appropriate to the remaining two surfaces. The computational advantages of the matrix method result from the fact that the problem rank is independent of the number of layers, and from the availability of personal computer software that makes interactive numerical experimentation with complex layered structures practical.<<ETX>>

PC software for SAW propagation in anisotropic multilayers

A software package that provides an interactive and graphical environment for surface acoustic wave (SAW) and plate-mode propagation studies in arbitrarily oriented anisotropic and piezoelectric multilayers is described. The software, which runs on an IBM PC with math coprocessor, is based on a transfer-matrix formulation for calculating the characteristics of SAW propagation in multilayers that was originally written for a mainframe computer. The menu-driven software will calculate wave velocities and field variable variations with depth for any desired propagation direction: the graphics capability provides a simultaneous display of slowness or velocity and of SAW Delta v/v coupling constant curves, and their corresponding field profiles in either polar or Cartesian coordinates, for propagation in a selected plane or as a function of one of the Euler angles. The program generates a numerical data file containing the calculated velocities and field profile data. Examples illustrating the usefulness of the software in the study of various SAW and plate structures are presented.<<ETX>>

High velocity pseudosurface waves (HVPSAW)

Current interest in low-loss UHF filters for use in mobile and personal communication systems has led to a number of pseudo-SAW (PSAW) and SH mode based SAW devices. These filters can operate at higher frequencies than SAW-based ones for a given line-width because PSAW and SH mode velocities can be significantly higher than corresponding SAW velocities. Furthermore for certain orientations the attenuation of the PSAW is acceptably small. In this paper the existence of an independent high-velocity pseudo-SAW (HVPSAW) mode is discussed. The HVPSAW is shown to have a phase velocity close to the longitudinal bulk wave velocity and to be quasi-longitudinally polarized. The nature of this HVPSAW mode is described for both electrically open-circuited and layered metallic short-circuited conditions for several piezoelectric materials. Numerical and experimental data are presented which discuss the existence and properties of these high-velocity pseudosurface waves.<<ETX>>

Electromechanical coupling to Lamb and shear-horizontal modes in piezoelectric plates

Recent theoretical studies and experiments have been shown that interdigital transducers can couple strongly to plate modes in piezoelectric materials and in piezoelectric-on-nonpiezoelectric composite membranes. The calculated velocity dispersion and electromechanical coupling factors for plate modes in representative piezoelectric materials are described. The frequency dependence of velocity and electromechanical coupling factors are given, under different metallization conditions, for generalized stiffened-Lamb, pure stiffened-Lamb, and stiffened-shear (shear-horizontal) modes, for various plate orientations in lithium niobate, lithium tantalate, quartz, bismuth germanium oxide, and zinc oxide. For lithium niobate, electromechanical-coupling values as high as 15% are found under narrowband bandpass conditions, and 5% under wideband low-pass conditions. For lithium tantalate, bismuth germanium oxide, coupling values of 0.5, 2, and 4% are obtained. For quartz with its weaker piezoelectricity, the coupling is still made smaller.<<ETX>>

Surface and pseudo surface acoustic waves in langatate: predictions and measurements

Langatate (LGT, La/sub 3/Ga/sub 5.5/Ta/sub 0.5/O/sub 14/) is a recent addition to materials of the trigonal crystal class 32. In this paper SAW contour plots of the phase velocity (v/sub p/), the electromechanical coupling coefficient (K/sup 2/), the temperature coefficient of delay (TCD), and the power flow angle (PFA), are given showing the orientations in space in which high coupling is obtained, with the corresponding TCD, PFA, and vp characteristics for these orientations. This work reports experimental results on the SAW temperature fractional frequency variation (/spl Delta/f/fo) and the TCD for several LGT orientations on the plane with Euler angles: (0/spl deg/, 132/spl deg/, /spl psi/). The temperature behavior has been measured directly on SAW wafers from 10 to 200/spl deg/C, and the results are compared with numerical predictions using our recently measured temperature coefficients for LGT material constants. This research also has uncovered temperature compensated orientations, which we have experimentally verified with parabolic behavior, turnover temperatures in the 130 to 160/spl deg/C range, and /spl Delta/f/fo within 1000 ppm variation from 10 to 260/spl deg/C, appropriate for higher temperature device applications. Regarding the pseudo surface acoustic waves (PSAWs), results of calculations are presented for both the PSAW and the high velocity PSAW (HVPSAW) for some selected, rotated cuts. This study shows that propagation losses for the PSAWs of about 0.01 dB/wavelength, and phase velocities approximately 20% higher than that of the SAW, exist along specific orientations for the PSAW, thus showing the potential for somewhat higher frequency SAW device applications on this material, if required.

ZnO on diamond: SAWs and pseudo-SAWs

The development of low-loss UHF SAW filters has led to devices using the higher phase velocities of pseudo-surface-acoustic-waves and shear-horizontally polarized waves. Another way of obtaining higher velocities is to use higher-velocity materials. Diamond, for example, has a SAW velocity near 11 km/s and a longitudinal velocity close to 18 km/s. In this paper the dispersion characteristics and the SAW coupling constants of the ZnO on diamond structure are described for the two lowest order modes and for the high-velocity pseudo-SAW mode. The SAW coupling constants are given for the four possible transducer geometries. At constant thickness-frequency, for the two lowest order modes, an unexpectedly large coupling (2/spl Delta/v/v) is found over a certain range of layer thickness-frequency product; 23% for the first mode and 15% for the second. Because of dispersion, calculating coupling at constant thickness-wavenumber (as is done frequently) produces results which are nearly four times smaller than those calculated at constant thickness-frequency.

High velocity pseudo surface waves (HVPSAW)

Current interest in low-loss UHF filters for use in mobile and personal communication systems has led to a number of pseudo-SAW (PSAW) and SH mode based SAW devices. These filters can operate at higher frequencies than SAW-based ones for a given line-width because PSAW and SH mode velocities can be significantly higher than corresponding SAW velocities. Furthermore for certain orientations the attenuation of the PSAW is acceptably small. In this paper the existence of an independent high-velocity pseudo-SAW (HVPSAW) mode is discussed. The HVPSAW is shown to have a phase velocity close to the longitudinal bulk wave velocity and to be quasi-longitudinally polarized. The nature of this HVPSAW mode is described for both electrically open-circuited and layered metallic short-circuited conditions for several piezoelectric materials. Numerical and experimental data are presented which discuss the existence and properties of these high-velocity pseudo surface waves

SAW and pseudo-SAW properties using matrix methods

A review of the basic features of surface acoustic waves (SAWs) and pseudo-SAWs (PSAWs) using the matrix method is presented. The mechanically free open-circuited and short-circuited surface wave boundary value problems for piezoelectrics are formulated. Two of the three possible types of modes (SAW and slow-PSAW) are described, and a number of computationally simple, frequency-independent analytical functions are derived. The relationship of these functions to the effective permittivity concept is demonstrated, and illustrative numerical examples for slow-PSAWs reveal that low-loss orientations are quite sensitive to material constant values.<<ETX>>Pseudo-surface-waves (PSAWs), or leaky SAWs, were first recognized over 25 years ago and the phase velocity (v/sub p/) and attenuation per wavelength (/spl alpha//spl lambda/) of PSAW modes for nonpiezoelectrics were calculated soon after. Since the seventies progress has been made in exploiting the higher velocities and electromechanical coupling constants (K/sup 2/=2/spl Delta/v/v) achievable with PSAWs for piezoelectric device applications; this has stimulated new interest in the search for piezoelectric materials with orientations which have low /spl alpha//spl lambda/, high K/sup 2/, high v/sub p/. Procedures for calculating the PSAW properties (v/sub p/, /spl alpha//spl lambda/, and K/sup 2/) are not very explicitly given. In light of the preceding we present in this paper a review of the basic features of SAW and PseudoSAWs using the matrix method. In this paper: the mechanically free open-circuited and short-circuited surface wave boundary value problems for piezoelectrics are formulated using the matrix method; two types of modes (SAW and PSAW) are described; and a number of computationally simple, frequency independent analytical functions are derived, from which /spl alpha//spl lambda/, v/sub p/, and K/sup 2/ are calculated for any direction on any material plane using commercially available PC software. The relationship of these functions to the effective permittivity concept, favoured by many researchers, is demonstrated and illustrative numerical examples for the PSAWs reveals that low-loss orientations are quite sensitive to material constant values.<<ETX>>

Arbitrarily oriented SAW gratings: network model and the coupling-of-modes description

A network model for surface-acoustic-wave (SAW) structures fabricated along arbitrary and hence nonsymmetric orientations, including natural single-phase unidirectional transducer (NSPUDT) directions, is described. From the predictions of this model for SAW gratings. the frequently used coupling of modes (COM) phenomenological description is evaluated. The network model consists of the usual sequence of mismatched transmission lines with susceptance loading at discontinuities to account for energy storage, plus a new additional reactive element calculated using a perturbation formula, to account for the asymmetry that exists for arbitrary orientations. The circuit elements are determined by geometrical and material parameters. It is demonstrated that the incremental COM description can be derived from the unit-cell-based network model, and analytical formulas quoted in the literature for the COM coefficients are compared with the values calculated from the ABCD network model description. An analytically tractable approximation for the network model is also described, from which rather simple explicit formulas for the COM coefficients that predict their dependence on material parameters and on frequency are derived. The analysis and numerical calculations indicate that these formulas may yield results that are valid over almost 30% relative bandwidths.<<ETX>>

Interactive PC software for SAW propagation in anisotropic multilayers

A software package which provides an interactive, graphical, and computational environment for surface-acoustic wave (SAW) and plate-mode propagation studies in arbitrarily oriented anisotropic and piezoelectric multilayers is described. The software, which runs on an IBM PC with maths coprocessor, is based on a transfer-matrix formulation for calculating the characteristics of SAW propagation in multilayers, originally written for a mainframe computer. The menu-driven software will calculate wave velocities and field variable variations with depth for any desired propagation direction; the graphics capability provides a simultaneous display of slowness or velocity and of SAW Delta v/v coupling constant curves and their corresponding field profiles in either polar or Cartesian coordinates for propagation in a selected plant or as a function of one of the Euler angles. The program generates a numerical data file containing the calculated velocities and field profile data. Examples illustrating the usefulness of the software in studying various SAW structures are presented.<<ETX>>