Dispersion Of Surface Acoustic Waves Research Articles

Investigation of phonons and magnons in [Ni80Fe20/Au/Co/Au] N multilayers

The interaction between phonons and magnons is a rapidly developing area of research, particularly in the field of acoustic spintronics. To discuss this interaction, it is necessary to observe two different waves (acoustic and spin waves) with the same frequency and wavelength. In the Ni80Fe20/Au/Co/Au system deposited on a silicon substrate, we observe the interaction between spin waves and surface acoustic waves using Brillouin light scattering spectroscopy. As a result, we can selectively control (activate or deactivate) the magnetoelastic interaction between the fundamental spin wave mode and surface acoustic waves. This is achieved by adjusting the magnetostrictive layer thickness in the multilayer. We demonstrate that by adjusting the number of layers in a multilayer structure, it is possible to precisely control the dispersion of surface acoustic waves while having minimal impact on the fundamental spin wave mode.

Simultaneous Determination of Young's Modulus and Density of Ultrathin Low‐k Films Using Surface Acoustic Waves

The nondestructive testing (NDT) of mechanical properties in ultrathin low dielectric constant (low‐k) films is a major challenge in integrated circuit manufacturing. Young's modulus and density are closely related parameters for low‐k films. This study presents a method for NDT of Young's modulus and density of porous low‐k black diamond (SiOC:H, BD) films. A linear frequency modulation (LFM) surface acoustic wave (SAW) interdigital transducer (IDT) with a frequency range of 20–250 MHz is designed to generate SAW signals on the samples. The series of SAW waveforms obtained on the samples are processed to obtain experimental SAW dispersion curves across a broad frequency range. By comparing these experimental curves with theoretical dispersion curves, as well as their first‐order derivatives, Young's modulus and density of porous low‐k BD films with thicknesses of 100, 300, 500, and 1000 nm are characterized. To verify Young's modulus measurements from the SAW method, a control experiment using nanoindentation is conducted. The results demonstrate that the SAW method can reduce the impact of the substrate and is independent of the film thickness. This study presents a highly accurate measuring method for simultaneous multiparameter evaluation of ultra‐thin low‐k films.

Investigation of acoustoelastic surface acoustic waves in prestressed media

Dispersion of broadband surface acoustic waves (SAWs) is often used for the nondestructive evaluation of near-surface elastic properties of materials. The accurate forward model of SAW propagation is essential for inversion. In this paper, we present a combining semi-analytical finite element (SAFE) and perfectly matched layer method for accurately predicting the phase velocity dispersion, attenuation and polarization modes of SAWs in any prestressed anisotropic layered half-space. Equations of motion are formulated based on the Biot's theory of small deformations influenced by initial stress, so it does not matter whether the residual stress results from hyperelastic transformations. The simulated results are firstly validated by the solutions from the exact three-dimensional elasticity theory-based method. The SAFE method is then used to discuss the effect of material anisotropy and residual stress on the SAWs. Finally, the method is applied to two practical examples. The differences and similarities of two common types of acoustoelastic theories are also discussed.

Laser Ultrasonic Automatic Detection Method for Surface Microcracks on Metallic Cylinders

Metallic cylinders are widely used in various fields of industrial production, and the automatic detection of surface microcracks is of great significance to the subsequent grinding process. In this paper, laser-excited surface acoustic waves (SAW) are used to detect surface microcracks. Due to the dispersion of SAWs on the cylinder surface, the SAWs exhibit different polarities at different positions. In order to improve the consistency of signals and the accuracy of the modeling, the angle at which the polarity is completely reversed is selected as the detection point. A laser ultrasonic automatic detection system is established to obtain signals, and the B-scan image is drawn to determine the location of the microcrack. By comparing the time–frequency diagrams of the reflected SAWs and transmitted SAWs, the transmitted wave is chosen to establish the microcrack depth prediction model. In addition, according to the trajectory of the grinding wheel, a prediction model based on the absolute depth of the microcracks is established, and the influence of the orientation of the microcracks on the signal energy is considered. The method proposed in this paper can provide a reference for the rapid grinding of microcracks on the surface of metallic cylinders; it has the characteristics of visualization and high efficiency, and overcomes the shortcomings of the currently used eddy current testing that provides information on the depth of microcracks with difficulty.

Refraction, beam splitting and dispersion of GHz surface acoustic waves by a phononic crystal

We exploit a time-resolved ultrafast optical technique to study the propagation of point-excited surface acoustic waves on a microscopic two-dimensional phononic crystal in the form of a square lattice of holes in a silicon substrate. Constant-frequency images and the dispersion relation are extracted, and the latter measured in detail in the region around the phononic band gap. Mode conversion and refraction at the interface between the phononic crystal and surrounding non-structured silicon substrate is studied at constant frequencies. Symmetric phonon beam splitting, for example, is shown to lead to a striking Maltese-cross pattern when phonons exit a square region of phononic crystal excited near its center.

Nondestructive Determination of Young's Modulus of Interconnecting Thin Films by a Broadband Surface Acoustic Wave‐Interdigital Transducer

A facile and rapid method for nondestructive testing (NDT) of the Young's modulus of interconnecting thin films using a broadband surface acoustic wave‐interdigital transducer (SAW‐IDT) is presented herein. A linear periodic SAW‐IDT with 20–125 MHz is designed and fabricated to excite surface acoustic wave (SAW) signals on the samples. By applying burst excitations under different frequencies, the SAW waveforms are picked up by a miniaturized piezoelectric transducer and processed by slant stack transformation. Consequently, the SAW dispersion curves over a wide frequency band are established to match the film parameters. Young's modulus of the 100 and 300 nm thickness of SiO2 films and the 800 and 1500 nm low‐k polyimide (PI) films is characterized. The nanoindentation method, as a control experiment, is also carried out to verify the accuracy of the SAW method, and the test results show that the SAW method can eliminate the effect of the substrate with higher precision. This work shows the advantage of the NDT technique by SAW‐IDT in measuring the Young's modulus of ultrathin films with low cost, controllable frequency range, and high accuracy.

Laser Ultrasound Investigations of AlScN(0001) and AlScN(11-20) Thin Films Prepared by Magnetron Sputter Epitaxy on Sapphire Substrates.

The laser ultrasound (LU) technique has been used to determine dispersion curves for surface acoustic waves (SAW) propagating in AlScN/Al2O3 systems. Polar and non-polar Al0.77Sc0.23N thin films were prepared by magnetron sputter epitaxy on Al2O3 substrates and coated with a metal layer. SAW dispersion curves have been measured for various propagation directions on the surface. This is easily achieved in LU measurements since no additional surface structures need to be fabricated, which would be required if elastic properties are determined with the help of SAW resonators. Variation of the propagation direction allows for efficient use of the system’s anisotropy when extracting information on elastic properties. This helps to overcome the complexity caused by a large number of elastic constants in the film material. An analysis of the sensitivity of the SAW phase velocities (with respect to the elastic moduli and their dependence on SAW propagation direction) reveals that the non-polar AlScN films are particularly well suited for the extraction of elastic film properties. Good agreement is found between experiment and theoretical predictions, validating LU as a non-destructive and fast technique for the determination of elastic constants of piezoelectric thin films.

Dispersion of surface acoustic waves in thin films at extreme wavelength-to-thickness ratios.

Surface acoustic waves (SAWs) are sensitive to the presence of a layer on the surface of a material, even if this layer is extremely thin compared to their wavelengths. Given the very slow propagation velocities of SAWs compared to electromagnetic waves, their wavelengths are on the order of 40 μm for acoustic frequencies on the order of 100 MHz. However, it has been shown that these waves are dispersive for coatings whose thicknesses are more than 1000 times smaller than their wavelength. This sensitivity is verified by studying the dispersion of SAWs for a frequency range between 90 and 260 MHz.

Study on dispersion and attenuation of laser-induced surface acoustic wave by grinding surface roughness

The dispersion and attenuation of surface acoustic wave (SAW) are important indicators for evaluating the damage of machined surface layer. However, the dispersion and attenuation of SAW is also affected by surface roughness. The finite element method can simulate the rough surface without surface damage. Based on the measured surface profiles of roughness profiler, a series of grinding surfaces of C45E steel with different surface roughness Ra are simulated by finite element method, and the dispersion and attenuation of laser-induced SAW are studied. It is found that with the increase of roughness Ra, the increase of dispersion is relatively uniform, while the increase of attenuation not. The possible reason is that the dispersion is mainly affected by the average amplitude of roughness, while the occasional deep valley profile has a great influence on the attenuation. Compared with the experimental data, it is found that the velocity variation of 10–40 MHz SAW caused by Ra 0.12–0.75 μm surface roughness accounts for 8%–19% of the total velocity variation, and the proportion increases with the increase of roughness. The attenuation of 15 MHz SAW caused by surface roughness accounts for 8%–13% of the total attenuation. For a rough surface, dispersion is approximately linear with the frequency of SAW, while the attenuation coefficient increases sharply with the increase of frequency. Therefore, it is necessary to first evaluate the influence of surface roughness, especially the influence on attenuation, when the dispersion and attenuation of SAW are used to evaluate the machined surface damage. The results of this paper can be used to evaluate the influence of roughness on the dispersion and attenuation of SAW, and reduce the deviation in the evaluation of machined surface damage.

Evaluation of Adhesion Properties of Thin Film Structure through Surface Acoustic Wave Dispersion Simulation.

A theoretical simulation study of the dispersion characteristic of the surface acoustic wave (Rayleigh wave) was conducted by modeling the adhesion interlayer with stiffness coefficients to evaluate the bonding properties of nano-scale thin film structures. For experimental validation, a set of thin film specimens were fabricated—637 nm, 628 nm, 637 nm, 600 nm, and 600 nm thick titanium (Ti) films were deposited on silicon (Si) (100) substrate using a DC Magnetron sputtering process with DC power from 28.8 W, 57.6 W, 86.4 W, 115.2 W, and 144 W. The thicknesses of the Ti films were measured using a scanning electron microscope (SEM). Surface acoustic wave velocity for each of the manufactured thin film specimens was measured by using a V(z) curve technique of a Scanning Acoustic Microscope. The measured velocity, transducer frequency, and thickness of the film were applied to dispersion characteristic simulation for a given stiffness coefficient to calculate adhesion strength of each specimen. To verify the simulation result, the adhesion force of each specimen was measured using a nano-scratch test and then compared with the calculated values from the dispersion characteristic simulation. The value of adhesion strength from the dispersion characteristic simulation and the value of adhesion force of the nano-scratch test were found to have a similar tendency according to the process variable of the thin film. The results demonstrated that the adhesion strength of a thin film could be evaluated quantitatively by calculating the dispersion characteristics with the adhesion interlayer stiffness model.

Evaluation of thermal material properties based on SAW dispersion in the laser-induced dynamic subsurface temperature gradient

Dispersion of surface acoustic waves (SAWs) caused by a dynamic surface heating–cooling cycle has been applied for evaluation of thermal properties. A laser-generated broad-band SAW pulse is propagated through the material whose elastic properties and density were modified by the dynamic inhomogeneous temperature field produced by laser heating and subsequent cooling. A sample with depth-dependent material properties introduces a phase velocity dispersion in SAW propagation. Dispersion was measured by a differential technique, which helped to isolate the thermally induced dispersion and eliminate the contributions of other possible sources of dispersion. The dispersion curves were measured at several time instants, which allowed evaluation of the following parameters: thermal diffusivity, temperature dependence of the shear modulus, and the temperature magnitude. The inverse problem was solved by fitting the experimental dispersion curves into the theoretical ones by means of differential evolution techniques.

Surface acoustic wave attenuation in polycrystals: Numerical modeling using a statistical digital twin of an actual sample

Grain boundary scattering-induced attenuation and phase-velocity dispersion of Rayleigh-type surface acoustic waves are studied with a time-domain finite-element method (FEM). The FEM simulation incorporates a realistic material model based on matching the spatial two-point correlation function of a Laguerre tessellation with that obtained from optical micrographs of a previously studied aluminum sample. Plane surface acoustic waves are excited in a multitude of statistically equivalent virtual polycrystals, and their surface displacement fields are averaged for subsequent extraction of the coherent-wave attenuation coefficient and phase velocity. Comparisons to previous laser-ultrasonic experiments, an analytical mean-field model, and the FEM results show good agreement in a broad frequency range from about 10 to 130MHz. Observed discrepancies between models and measurement reveal the importance of spatial averaging in the context of mean-field approaches and suggest improvement strategies for future experimental studies and advanced analytical models. A different attenuation power law for Rayleigh waves is found in the stochastic scattering regime compared to bulk acoustic waves.

Synchrosqueezed wavelet transform-based method for characterizing the dispersive nature of laser-excited surface acoustic waves propagating through the coated or damaged medium

Dispersion of surface acoustic waves (SAWs) can be used for determination of the mechanical parameters of the film or the damaged layer. The correct evaluation of the experimental dispersion curves is important for backcalculation. In this paper, we present a method to identify experimental dispersion curves from two-station time-varying signals based on time–frequency analysis. Synchrosqueezed wavelet transform (SWT) provides the quantitative description of the propagation of different frequency components of SAWs. Discrete phase velocity estimation is accomplished based on the cross-correlation function. Rényi entropy-based SWT spectrum noise reduction and cosine interpolation are applied for improving the quality of dispersion curves. An example is presented to illustrate the application of the proposed method. Finally, laser ultrasonic experiments are performed on the surface of three typical test samples. The comparison of the resulting dispersion curves shows the effectiveness of the proposed method and the necessity of noise reduction and interpolation.

Dimensional and mechanical characterization of metallic thin films based on the measurement of surface acoustic waves dispersion with Slant Stack transform

In this study, an ultrasonic method for characterizing thin films based on the dispersion of the first Rayleigh mode is presented. The principle of surface acoustic waves (SAW) generation using a broadband transducer and their detection is detailed. It is shown that over a frequency range between 20 MHz and 125 MHz, SAWs are sensitive to fine deposits and the attenuation is reasonable thus enabling measurements over 20 mm. The Slant Stack transform used to obtain the experimental dispersion curves with excellent signal-to-noise ratios is then presented and analyzed. Finally, four samples of silicon on which gold layers 400 nm, 300 nm, 180 nm, and 50 nm thick had been deposited and characterized. The thicknesses and the elastic parameters of the gold layers and the silicon substrate were obtained from the inversions performed on the experimental dispersion curves. These results show the efficiency of the non-destructive ultrasonic technique associated with a Slant Stack transform before inversion.

A Transient Grating Method to Measure the Dispersion of Elastic Waves in Nanostructures

We describe the so-called “Transient Grating Method” which is a non-invasive experimental technique well suited to measure the dispersion properties of ordered or disordered nanostructures and thin films, at frequencies up to a few GHz. This pump-and-probe technique involves the interference pattern produced by two in-coming IR optical pulses to set a standing elastic wave on the surface of the sample through photoelastic processes. The wave vector of this elastic wave can be easily tuned by adjusting the angle between the two incident beams. Two continuous visible laser beams in a heterodyne detection scheme are used to detect the vibrations on the surface and in turn the dispersion of the related elastic modes. The achievements of the technique are illustrated by the measurement of the dispersion of surface acoustic waves in piezogenerators consisting of GaN nanowires embedded into a dielectric matrix (HSQ). We then report on the analysis of the experimental data that allowed extracting the elastic parameters of this composite medium.

Experimental determination of the electro-acoustic properties of thin film AlScN using surface acoustic wave resonators

In this work, all electroacoustic material parameters, i.e., the elastic, piezoelectric, and dielectric coefficients, as well as the mass density, were determined experimentally for wurtzite aluminum scandium nitride (Al1−xScxN) for a wide range of Sc concentrations of up to x = 0.32 from the same material source for the first time. Additionally, the mass density and piezoelectric coefficient were determined even up to x=0.42. Two sets of 1 μm-thick AlScN(0001) thin films were deposited on Si(001) using reactive pulsed-DC magnetron cosputtering. One set of thin films was used to determine the a- and c- lattice parameters and the effective relative dielectric coefficient ε33,f, using X-ray diffraction and capacitive measurements, respectively. Lattice parameters were then used to extract average internal parameter u, bond length, and bond angle, as well as mass density, as a function of Sc concentration. Density functional theory calculations were performed to provide the equilibrium lattice parameters a, c, and u, as well as the bond angle and the bond lengths for wurtzite-AlN and layered hexagonal-ScN. The second set of films was used to fabricate surface acoustic wave (SAW) resonators with wavelengths λ from 2 up to 24 μm. The SAW dispersion in conjunction with finite element modeling fitting was used to extract the elastic stiffness as well as the piezoelectric coefficients. The overall evolution of the material parameters and the change of the crystal structure as a function of Sc concentration is discussed in order to provide a possible explanation of the observed behavior.

THERMAL MODEL FRO SAW CALCULATIONS IN THE LAYERED SYSTEMS

The calculation of surface acoustic wave (SAW) parameters in the layered systems consists of half infinite substrate and one or several layers when the temperature is variable have been considered. SAW phase velocity calculation with temperature dependent material constants have been discussed. Expressions for the temperature coefficients of delay (TCD) and the temperature coefficients of frequency (TCF) of the first and the second order with taking into account SAW dispersion have been evaluated. Numerical procedures for TCD and TCF calculation have been proposed.

Feasibility study of using the dispersion of surface acoustic wave impulse for viscoelasticity characterization in tissue mimicking phantoms

The aim of this study was to investigate the feasibility of utilizing the phase velocity dispersion of impulse surface acoustic wave (SAW) for viscoelasticity characterization of soft materials. The focused ultrasound transducer and the phase-sensitive optical coherence tomography were applied as the impulse SAW inducer and tracker, respectively. Three types of liquid-paraffin-based cream-in-agar phantoms were tested. Phase velocity dispersion curve was extracted using a Fourier transform-based phase velocity analysis algorithm. Viscoelastic parameters were obtained by fitting the dispersion curve of SAW into Rayleigh wave dispersion equation. The estimated viscoelasticity was compared with that from spherical indenter, ramp-hold relaxation testing for validation. Both results show an increasing trend in the elasticity and decreasing trend in the viscosity with the concentration of liquid-paraffin-based cream increasing in the samples. The proposed method has the capability of evaluating the viscoelastic properties of homogeneous soft tissue. By combining viscoelastic parameters estimated from the proposed method, the dispersive SAW-impulse-based viscosity-compensated elastography could be further developed.

Features of acoustic wave propagation in the Me/ZnO/Me/diamond waveguide structure.

The effect of mass loading on the phase velocities of the surface acoustic wave dispersion modes in the Me/ZnO/Me/diamond piezoelectric layered structure as a function of frequency, metallic, and piezoelectric layer thickness has been investigated. Aluminum, molybdenum, and platinum were considered as the metallic layer materials. It has been demonstrated that the change in the phase velocities substantially depends on the acoustic impedance of the metal layer and its thickness. Results obtained can be useful in the development of controlled acoustoelectronic devices and sensors operating on the Rayleigh and Love waves.

Complex dispersion relation of surface acoustic waves at a lossy metasurface

The complex dispersion relation of surface acoustic waves (SAWs) at a lossy resonant metasurface is theoretically and experimentally reported. The metasurface consists of the periodic arrangement of borehole resonators in a rigid substrate. The theoretical model relies on a boundary layer approach that provides the effective metasurface admittance governing the complex dispersion relation in the presence of viscous and thermal losses. The model is experimentally validated by measurements in the semi-anechoic chamber. The complex SAW dispersion relation is experimentally retrieved from the analysis of the spatial Laplace transform of the pressure scanned along a line at the metasurface. The geometrical spreading of the energy from the speaker is accounted for, and both the real and imaginary parts of the SAW wavenumber are obtained. The results show that the strong reduction of the SAW group velocity occurs jointly with a drastic attenuation of the wave, leading to the confinement of the field close to the source and preventing the efficient propagation of such slow-sound surface modes. The method opens perspectives to theoretically predict and experimentally characterize both the dispersion and the attenuation of surface waves at structured surfaces.