Power Flow Angle Research Articles

X-ray diffraction analysis of the surface acoustic wave propagation in langatate crystal

X-ray diffraction on a langatate crystal (La3Ga5.5Ta0.5O14, LGT) modulated by a Λ=12 μm Rayleigh surface acoustic wave (SAW) was studied in a double axis X-ray diffractometer scheme at the BESSY synchrotron radiation source. SAW propagation in the crystal causes sinusoidal modulation of the crystal lattice and the appearance of diffraction satellites on the rocking curves, with their number, angular positions, and intensities depending on the wavelength and amplitude of acoustic vibrations of the crystal lattice. Strong absorption of X-ray radiation in LGT enables the observation of the diffraction spectra extinction at certain SAW amplitudes. X-ray diffraction spectra analysis makes it possible to determine SAW amplitudes and wavelengths, to measure the power flow angles, and investigate the diffraction divergence in acoustic beam in LGT.

The power flow angle of acoustic waves in thin piezoelectric plates

The curves of slowness and power flow angle (PFA) of quasi-antisymmetric (A(0)) and quasi-symmetric (S(0)) Lamb waves as well as quasi-shear-horizontal (SH(0)) acoustic waves in thin plates of lithium niobate and potassium niobate of X-,Y-, and Z-cuts for various propagation directions and the influence of electrical shorting of one plate surface on these curves and PFA have been theoretically investigated. It has been found that the group velocity of such waves does not coincide with the phase velocity for the most directions of propagation. It has been also shown that S(0) and SH(0) wave are characterized by record high values of PFA and its change due to electrical shorting of the plate surface in comparison with surface and bulk acoustic waves in the same material. The most interesting results have been verified by experiment. As a whole, the results obtained may be useful for development of various devices for signal processing, for example, electrically controlled acoustic switchers.

SAW Parameters on Y-cut Langasite Structured Materials

This paper presents results and investigations of several new, man-made piezoelectric single crystal, Czochralski-grown substrate materials for surface acoustic waves (SAW) applications. These materials, langanite (LGN), langatate (LGT), Sr3TaGa3Si2O14 (STGS), Sr3NbGa3Si2O14 (SNGS), Ca3TaGa3Si2O14 (CTGS), and Ca3NbGa3Si2O14 (CNGS), have the same structure as langasite (LGS) and are of the same crystal class as quartz. These compounds are denser than quartz, resulting in lower phase velocities. They also have higher coupling. Unlike quartz and lithium niobate, there is no degradation of material properties below the material melting points resulting in the possibility of extreme high-temperature operation (> 1000 degrees C). This paper gives a summary of extracted SAW material parameters for various propagation angles on Y-cut substrates of the six materials. Parameters included are electromechanical coupling, phase velocity, transducer capacitance, metal strip reflectivity, and temperature coefficient of frequency. Using previously published fundamental material constants, extracted parameters are compared with predictions for LGT and LGN. In addition, power flow angle and fractional frequency curvature data are reported for propagation angles on CTGS and CNGS Y-cut substrates that exhibit temperature compensation near room temperature. Detailed descriptions of the SAW parameter extraction techniques are given. A discussion of the results is provided, including a comparison of extracted parameters and an overview of possible SAW applications.

Power Flow Angles for Slanted Finger Surface Acoustic Wave Filters on Langasite Substrate

Power flow angles (PFAs) on a langasite (LGS) substrate with Euler angles of (0°, 138.5°, ψ), ψ=25.7 to 27.7° are investigated for slanted finger interdigital transducer (SFIT) surface acoustic wave (SAW) filters by an electrical and optical methods. In the electrical method, several tilted SFIT SAW filters with different tilt angles for (0°, 138.5°, ψ) LGS substrates were designed, and the frequency responses of the filters were measured. In the optical method, the PFAs were directly measured by optical probing for a parallel interdigital transducer (IDT) with wide propagation area on the substrate. As a result, a good correlation between electrical and optical measurements of the PFAs is obtained, but the calculated PFAs are slightly different from the measured PFAs. A good frequency response of a tilted 380 MHz SFIT SAW filter with an appropriate tilt angle corresponding to the PFA on the substrate is obtained even though the aperture is small.

Optimal selection of piezoelectric substrates and crystal cuts for SAW-based pressure and temperature sensors

In this paper, the perturbation method is used to study the velocity shift of surface acoustic waves (SAW) caused by surface pressure and temperature variations of piezoelectric substrates. Effects of pressures and temperatures on elastic, piezoelectric, and dielectric constants of piezoelectric substrates are fully considered as well as the initial stresses and boundary conditions. First, frequency pressure/temperature coefficients are introduced to reflect the relationship between the SAW resonant frequency and the pressure/temperature of the piezoelectric substrates. Second, delay pressure/temperature coefficients are introduced to reflect the relationship among the SAW delay time/phase and SAW delay line-based sensors' pressure and temperature. An objective function for performance evaluation of piezoelectric substrates is then defined in terms of their effective SAW coupling coefficients, power flow angles (PFA), acoustic propagation losses, and pressure and temperature coefficients. Finally, optimal selections of piezo-electric substrates and crystal cuts for SAW-based pressure, temperature, and pressure/temperature sensors are derived by calculating the corresponding objective function values among the range of X-cut, Y-cut, Z-cut, and rotated Y-cut quartz, lithium niobate, and lithium tantalate crystals in different propagation directions.

Effect of metallization on the power flow angle of SH0 waves in thin piezoelectric plates

The anisotropy of the angle between the phase and group velocity (power flow angle, PFA) as well as the influence of electrical boundary conditions on this angle have been studied for shear-horizontal fundamental (SH0) acoustic waves in thin piezoelectric plates of lithium niobate (LNO) and potassium niobate (KNO). Both LNO and KNO crystals possess orientations at which the PFA for SH0 waves reaches large values (17° and 48°, respectively). It is established that metallization of the piezoelectric plate surface can significantly change PFA values, in particular, by 18° and 55° for Y-X + 25° cut plates of LNO and KNO, respectively.

Analyses and mitigation of spurious scattered signals in acoustic wave reflection measurements

Reflection techniques are widely used in extracting the acoustic wave (AW) constants and temperature coefficients of anisotropic crystals. To obtain these constants with the desired precision, care should be taken in the sample preparation, including flatness, parallelism and surface finishing or polishing. Not so obvious is that along some orientations, required for the extraction of elastic constants in anisotropic materials, the non-zero bulk acoustic wave (BAW) power flow angles (PFA) and related BAW multimode conversion and scattering at sample boundaries will generate spurious reflections. These spurious signals may interfere with the desired signals, significantly compromising the measurements. This paper reports on an original analysis that combines the effects of PFA, wave scattering, mode conversion, sample dimensions and transducer positioning in pulse echo measurements and on the importance of considering these effects in the design of the sample to be measured. Graphical and numerical analyses are used to fully explain the experimental data obtained using a 25 mm Y-cut quartz sample. Along this propagation direction, the longitudinal wave (5996.0 m/s) reflected from the back wall of the sample is detected at the transducer after approximately 8.3 and 16.7 μs. However, clearly identifiable spurious signals occur around 11.6 and 19.9 μs. These are direct consequences of the position of the transducer/buffer rod unit and thus the PFA. The correlation between the measured spurious pulse's response in time, the sample dimensions and the PFA is detailed in this paper. Based on the analyses performed, a sample dimension design method was developed and is uncovered in this paper, which aims at the mitigation of spurious signal interferences in pulse reflection measurements.

X-ray topography analysis of acoustic wave fields in the SAW-resonator structures

The formation of fields of standing surface acoustic waves (SAW) in LiNbO3 and La3Ga5SiO14 (LGS) crystals was studied by high-resolution topography method on a laboratory X-ray source. The fields of standing SAW were formed using SAW-resonator structures consisting of interdigital transducer (IDT) and reflecting gratings. The SAW amplitudes and power flow angles were measured by X-ray topography, diffraction in acoustic beam was visualized, and the SAW interaction with the crystal structure defects was studied.

Propagation Characteristics of Surface Acoustic Waves on K3Li2Nb5O15

The contour maps of the phase velocity vf, the temperature coefficient of delay (TCD), the electromechanical coupling coefficient K2, and the power flow angle (PFA) of surface acoustic waves (SAWs) on K3Li2Nb5O15 are presented for Euler angles (φ, θ, ψ) with φ=0, 10°, 20°, 30°, and 40°, and -180° ≤φ, θ< 180°. These maps computed by Campbell and Jonnes' method reveal that SAWs on K3Li2Nb5O15 with Euler angles (4°, 49°, 92°), (33°, 76°, 126°), and (30°, 86°, 151°) have vf of 3255 m/s, 3383 m/s, and 3728 m/s, K2 of 0.0115, 0.0147, and 0.0045, the values of first-order TCD of 0.02 ppm/°C, 0.05 ppm/°C, and 0.04 ppm/°C, and PFAs of 0.005°, 4.7°, and 5.1°, respectively.

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

Langatate (LGT, La3Ga(5.5)Ta(0.5)O14) is a recent addition to materials of the trigonal crystal class 32, which is the same crystal class as quartz, langasite, langanite, and gallium phosphate. Langatate has several attractive acoustical properties, in particular: a measured bulk acoustic wave (BAW) resonator quality factor frequency product (Qf) of 16 million, comparable to that of AT cut quartz; high-piezoelectric coupling orientations, up to 0.5% for surface acoustic waves (SAWs), about five times larger than that of ST-X quartz; low power flow angle orientations in the vicinity of high coupling orientations; phase velocities about 20% smaller than those of ST-X quartz, facilitating the production of smaller, lower frequency devices; the existence of pseudo SAW modes for higher frequency applications. In this paper SAW contour plots of the phase velocity (vp), the electromechanical coupling coefficient (K2), 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 (delta f/fo) and the TCD for several LGT orientations on the plane with Euler angles: (0 degrees, 132 degrees, psi). The temperature behavior has been measured directly on SAW wafers from 10 to 200 degrees 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 degrees C range, and delta f/fo within 1000 ppm variation from 10 to 260 degrees 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.

Comparison between ST-cut quartz 25 degrees and -60 degrees NSPUDT propagation directions.

This paper discusses directivity and other propagation properties of natural single phase unidirectional transducer (NSPUDT) propagation directions on ST-cut quartz. The work focuses on the comparison of surface acoustic wave (SAW) directivity and propagation properties between the ST-cut quartz -60 degrees, Euler angles: (0 degrees, 132.75 degrees, -60 degrees), and the ST-cut quartz 25 degrees, Euler angles: (0 degrees, 132.75 degrees, 25 degrees), NSPUDT propagation directions, including predicted and measured directivity responses for both propagation directions. The well-known SAW 25 degrees propagation direction is used for low loss, high performance SAW filter designs for consumer products and communications applications. The ST-cut quartz -60 degrees propagation direction has been predicted to have a reflection coefficient 2.5 times larger than ST-cut quartz 25 degrees. In addition the ST-cut quartz -60 degrees satisfied the NSPUDT 90 degrees reflection coefficient phase condition much more closely, resulting in an improved directivity response. For the delay line structures used in the experiments, the measured directivity is 10.1 dB for the -60 degrees propagation direction. For the same structures, the measured directivity along the 25 degrees propagation direction is about 5.0 dB. The experimental results given in this paper verify that indeed ST-cut quartz -60 degrees has a higher directivity than ST-cut quartz 25 degrees, confirming the theoretical predictions. In addition, this work compares other propagation properties for both directions, namely, phase velocities, electromechanical couplings, temperature coefficients of delay, power flow angles, and metallic strip reflection coefficient amplitudes and phases.

Metal strip reflectivity and NSPUDT orientations in langanite, langasite, and gallium phosphate.

New materials of the trigonal 32 class have received much attention recently, due to their quartz-like temperature behavior and the promise of higher electromechanical coupling coefficients. The magnitude and phase of the reflection coefficient of the metal strips that form the SAW transducers and reflector structures is a critical parameter that allows proper device designs and optimal material surface orientation. This paper describes an investigation of the magnitude and phase of the SAW metal strip reflectivity in some new materials and along new orientations. The materials are langanite, langasite, and gallium phosphate. The results are presented as contour plots of the magnitude and phase of the reflection coefficient. In addition, the phase velocity, temperature coefficient of delay, electromechanical coupling coefficient, and power flow angle are given, thus allowing proper orientation selection for SAW device designs. The results presented highlight the reflection coefficient calculations in the selection of natural single-phase unidirectional transducer orientations (NSPUDT) for these new materials. As a result of the present work, reflection coefficient magnitudes five times larger than those of the well-known quartz NSPUDT orientation (Euler angles: 0 degrees 132.75 degrees 25 degrees) can be obtained with the new materials, for orientations where the optimum NSPUDT reflection coefficient phase criterion is met. The new materials discussed here provide an opportunity to design shorter- and higher-bandwidth devices due to: the increased electromechanical coupling coefficient; the higher reflection coefficient; and the lower phase velocities; while maintaining the excellent temperature insensitivity characteristic of quartz. The orientation regions suggested in this paper for the new materials are thus very promising for low-loss, high-performance consumer and communications SAW designs, such as NSPUDT filters, resonator-based filters, and other devices that can benefit from a high metal strip reflectivity.

Optimal cuts of langasite, La3Ga5SiO14 for SAW devices.

The results of a theoretical and experimental investigation of the SAW propagation characteristics in an optimal region of langasite defined by the Euler angles phi from -15 degrees to +10 degrees, theta from 120 degrees to 165 degrees, and psi from 20 degrees to 45 degrees are presented. Based on temperature coefficients of the elastic constants derived from experimental data, some optimal orientations of langasite characterized by high electromechanical coupling factor (k2), zero power flow angle (PFA) and low or zero temperature coefficient of frequency (TCF) were found. The SAW velocity in the region of interest is highly anisotropic; this results in a significant amount of diffraction, which must be taken into account in the search for orientations useful for SAW devices. An orientation having simultaneously zero PFA, zero TCF, negligible diffraction, and relatively high piezoelectric coupling has been found and verified experimentally. The experimental results are in excellent agreement with the calculated SAW characteristics. The frequency response of a SAW device fabricated on the optimal cut of langasite is presented and demonstrates that high performance SAW filters can be realized on this optimal cut of langasite.

PSEUDO AND HIGH VELOCITY PSEUDO SAWs

This article discusses the characteristics of pseudo surface waves (PSAWs) and high velocity pseudo surface waves (HVPSAWs). The fundamental properties of these waves, the matrix method formulation, the different solution types due to crystal symmetry, early experiments on HVPSAWs, and practical applications of pseudo surface acoustic waves serve as an introduction. The solutions to the pseudo modes are discussed by analyzing the boundary condition function for several orientations. The relation between the radiating partial modes and the sagittal plane bulk slowness reveals new characteristics of the different symmetry types of HVPSAW, and helps classify and understand the pseudo modes. The acoustoelectric Poynting vector is used along different crystal symmetry orientations to reveal and discuss the pseudo SAW characteristics: penetration depth, declination of the power vector, and an estimation of power flow angle. Experimental data and numerical solutions of HVPSAW and PSAW along selected planes and orientations are discussed. This article concludes with a brief analysis of layered structures on different symmetry type substrates and a discussion of the layered pseudo surface wave properties.

Pseudo and High Velocity Pseudo SAWs

This article discusses the characteristics of pseudo surface waves (PSAWs) and high velocity pseudo surface waves (HVPSAWs). The fundamental properties of these waves, the matrix method formulation, the different solution types due to crystal symmetry, early experiments on HVPSAWs, and practical applications of pseudo surface acoustic waves serve as an introduction. The solutions to the pseudo modes are discussed by analyzing the boundary condition function for several orientations. The relation between the radiating partial modes and the sagittal plane bulk slowness reveals new characteristics of the different symmetry types of HVPSAW, and helps classify and understand the pseudo modes. The acoustoelectric Poynting vector is used along different crystal symmetry orientations to reveal and discuss the pseudo SAW characteristics: penetration depth, declination of the power vector, and an estimation of power flow angle. Experimental data and numerical solutions of HVPSAW and PSAW along selected planes and orientations are discussed. This article concludes with a brief analysis of layered structures on different symmetry type substrates and a discussion of the layered pseudo surface wave properties.

New Piezoelectric Substrates for SAW Devices

Recent developments in single crystal piezoelectric materials have focused on the search for "ideal" materials with zero temperature coefficient of frequency orientations featuring jointly high piezoelectric coupling, high intrinsic Q, zero power flow angle, and minimized diffraction effects. In addition, the desired materials should have no low temperature phase transitions, and a physical chemistry conducive to repeatable, low cost growth and wafer scale device production. As difficult as it might seem to find such "ideal" materials, three completely different but strong candidate materials have emerged recently: the quartz homeotype gallium orthophosphate, the quartz isotype calcium gallo-germanates (langasite, langanite, langatate, etc.), and diomignite (lithium tetraborate). The current state-of-the-art and prospects for future development of these materials are considered.

NEW PIEZOELECTRIC SUBSTRATES FOR SAW DEVICES

Recent developments in single crystal piezoelectric materials have focused on the search for "ideal" materials with zero temperature coefficient of frequency orientations featuring jointly high piezoelectric coupling, high intrinsic Q, zero power flow angle, and minimized diffraction effects. In addition, the desired materials should have no low temperature phase transitions, and a physical chemistry conducive to repeatable, low cost growth and wafer scale device production. As difficult as it might seem to find such "ideal" materials, three completely different but strong candidate materials have emerged recently: the quartz homeotype gallium orthophosphate, the quartz isotype calcium gallo-germanates (langasite, langanite, langatate, etc.), and diomignite (lithium tetraborate). The current state-of-the-art and prospects for future development of these materials are considered.

Investigation on recent quartz-like materials for SAW applications

Recent progress in growing and characterizing quartz-like materials of the trigonal system class 32 has been reported by several groups. The promising perspective for bulk acoustic wave frequency control applications indicates the potentiality of employing these materials for SAW applications as well. This paper reports results of investigations focused on SAW orientations of langasite (LGS), gallium phosphate (GaPO(4)), and langanite (LGN), both singly and doubly rotated cuts. Among the characteristics explored, major attention is paid to the temperature coefficient of delay (TCD), the electromechanical coupling coefficient (K(2)), and the power flow angle (PFA). Contour graphs are plotted based on our calculated results and show the regions in space in which low TCD and high K(2 ) can be obtained; they also exhibit the associated PFA and phase velocity characteristics. The influence of different sets of material constants is addressed. The spatial investigation performed shows that there are promising orientation regions in these materials at which zero or reduced TCD (<10 ppm/ degrees C) and PFA are obtained. Additional attractive characteristics for SAW applications have been observed: values of K(2) a few times higher than the K(2) of quartz ST-X, thus finding applications in larger bandwidth devices; variation of the TCD with respect to temperature, which is comparable to the variation found for quartz ST-X and less than that for zero TCD Li (2)B(4)O(7) cuts like 45 degrees X-Z and (0 degrees 78 degrees 90 degrees ); and phase velocity values circa 13 to 26% smaller than the phase velocity of quartz ST-X thus allowing a reduction in size for intermediate frequency device applications.

Analysis of Surface Acoustic Wave Properties of the Rotated Y-cut Langasite Substrate

The propagation characteristics of Rayleigh waves on a Y-rotated La3Ga5SiO14 (langasite) substrate are evaluated with the use of newly obtained material constants. The calculated phase velocity, the power flow angle (PFA), the coupling electromechanical coefficient (K2), the temperature coefficient of delay (TCD) and the diffraction coefficient (γ) are shown as contour maps. The revised numerical calculations were in much better agreement with the experimental results of the temperature characteristics on the langasite substrate with Euler angle (0°, 140°, φ). Moreover, the temperature characteristics as a function of the metal thickness were experimentally investigated. It was found that a thicker metal leads to a lower turnover temperature. Finally, an example of the frequency response of the transversal filter designed for IS95 is shown.

Surface acoustic wave properties of La3Ga5SiO14 crystals

The temperature-compensated Rayleigh SAW properties of La 3 Ga 5 SiO 14 LGS), including SAW velocity v, temperature coefficient of delay TCD, coupling coefficient k2 and power flow angle (PFA) were simulated. The results showed that only two propagation directions with zero TCD and large k2 of 0.36 and 0.41% were located around (0°, 140°, 25°) and (15°, 151° 40.5°), respectively. The experimental results gave a good agreement with the calculated one. The details about the two directions were discussed.