Nonlinear Surface Acoustic Waves Research Articles

Strong diffraction of nonlinear surface acoustic waves in crystals

Nonlinear distortion and shock formation in planar surface acoustic waves in anisotropic crystals have been modeled without [Hamilton et al., JASA (1999)] and with [Cormack et al., JASA 2022] piezoelectricity. Weak diffraction has been included in the paraxial approximation for nonlinear surface wave beams in isotropic solids [Shull et al., JASA (1995)]. Here, a procedure for including strong diffraction, i.e., without the paraxial approximation, in the model for nonlinear surface waves in crystals is presented, which incorporates the angular spectrum approach described by Kharusi and Farnell (JASA 1970). Anisotropy is defined by expressing the phase speed of a plane wave, and therefore, the magnitude of the corresponding wavenumber, as a function of the direction of propagation. Next, an explicit expression relating the two wavenumber components in the planar surface along which the wave propagates must be obtained as a function of direction, requiring iterative solution of a transcendental relation. The beam is then propagated incrementally away from the source, advancing the angular spectrum in k-space and including nonlinear interactions in the spatial domain to characterize the combined effects of diffraction and nonlinearity. Preliminary results are presented for converging nonlinear surface waves in crystals. [Work supported by IR&D at ARL:UT.]

Additive laser excitation of giant nonlinear surface acoustic wave pulses

Additive laser excitation of giant nonlinear surface acoustic wave pulses

Peridynamic modeling of nonlinear surface acoustic waves propagating in orthotropic materials

Due to the elastic nonlinearity of the material, high-amplitude surface acoustic waves undergo nonlinear evolution during propagation and may lead to material failure. To enable the acoustical quantification of material nonlinearity and strength, a comprehensive understanding of this nonlinear evolution is necessary. This paper presents a novel ordinary state-based nonlinear peridynamic model for the analysis of the nonlinear propagation of surface acoustic waves and brittle fracture in anisotropic elastic media. The relationship between seven peridynamic constants and second- and third-order elastic constants is established. The capability of the developed peridynamic model has been demonstrated by predicting surface strain profiles of surface acoustic waves after propagating in the silicon (111) plane and the 〈112¯〉 direction. On this basis, the nonlinear wave-induced spatially localized dynamic fracture is also studied. The numerical results reproduce the main features of nonlinear surface acoustic waves and fracture observed in experiments.

Strongly focused nonlinear surface acoustic wave beams in isotropic solids

A promising direction in the tailored control of quantum materials is the modification of their structure-function relationship via engineered laser-driven shock waves. In order to inform how the laser excitation should be tailored to optimize the effect of the shock waves, a model is desired for strongly focused nonlinear surface waves in crystals. A model was developed previously in the paraxial approximation for weakly diffracting nonlinear surface wave beams in isotropic solids [Shull et al., JASA 97, 2126 (1995)]. Harmonic generation and shock formation were investigated numerically in that work for sources with uniform amplitude distributions, with analytical solutions for the fundamental and second harmonic obtained for weakly focused Gaussian beams. Here, numerical results are reported for shock formation in focused nonlinear surface waves obtained using a model unrestricted by the paraxial approximation in order to accommodate strong focusing in isotropic solids. Removal of the restriction to isotropic solids is work in progress based on representation of the wave field in terms of its angular spectrum and a model for planar nonlinear surface waves in crystals [Hamilton et al., JASA 105, 639 (1999)]. [Work supported by the IR&D Program at Applied Research Laboratories.]

Fracture of single crystal silicon caused by nonlinear evolution of surface acoustic waves

High-amplitude surface acoustic waves (SAWs) undergo nonlinear sharpening during propagation due to the elastic nonlinearity of the material, which leads to material fracture. The degree of nonlinear evolution and material strength are usually characterized by two parameters: the second-order nonlinearity parameter and the critical fracture stress. To study the influence of processing defects, residual stress and temperature on these two parameters, we carry out molecular dynamics modeling of nonlinear propagation of SAWs on non-ideal surfaces. The Stillinger and Weber (SW) and the Lee-modified second nearest-neighbor modified embedded-atom-method (2NN MEAM) potentials are used to study the SAW nonlinear evolution and surface crack nucleation in silicon 1111¯1¯2 geometry, respectively. The results show that processing defects have the greatest influence on the SAW evolution and material strength. For a defined level of defects, the size of initial SAW wavelength directly affects the degree of attenuation of harmonic waves and stress concentration, and then determines the measured nonlinear parameter and critical stress. Temperature can affect the magnitude of the two characterization parameters through thermal dissipation and thermal fluctuations. In the presence of residual stresses only, the relative degree of variation of these two parameters is weak. This study may provide a valuable reference for the establishment of nonlinear SAW atomic-level theory and material characterization experiments.

Nonlinear piezoelectric surface acoustic waves.

The theory for nonlinear surface acoustic waves in crystals developed using Hamiltonian mechanics [Hamilton, Il'inskii, and Zabolotskaya, J. Acoust. Soc. Am. 105, 639 (1999)] is modified to account for piezoelectric material properties. The derived spectral evolution equations permit analysis of nonlinear surface wave propagation along a cut surface of any orientation with respect to the crystallographic axes and for piezoelectric crystals with any symmetry. Numerical simulations of waveform distortion in the particle velocity and electric field components are presented for surface wave propagation in Y-cut lithium niobate along the X- and Z-crystallographic axes. The influence of piezoelectricity is illustrated by comparing the nonlinear evolution of waveforms along a surface bounded by a vacuum (free space) and an ideal conductor (short circuit). Contributions to the nonlinearity from elasticity, piezoelectricity, electrostriction, and dielectricity are quantified separately for the two boundary conditions.

A nonlinear analysis of surface acoustic waves in isotropic elastic solids

With the fast evolution of wireless and networking communication technology, applications of surface acoustic wave (SAW), or Rayleigh wave, resonators are proliferating with fast shrinking sizes and increasing frequencies. It is inevitable that the smaller resonators will be under a strong electric field with induced large deformation, which has to be described in wave propagation equations with the consideration of nonlinearity. In this study, the formal nonlinear equations of motion are constructed by introducing the nonlinear constitutive relation and strain components in a standard procedure, and the equations are simplified by the extended Galerkin method through the elimination of harmonics. The wave velocity of the nonlinear SAW is obtained from approximated nonlinear equations and boundary conditions through a rigorous solution procedure. It is shown that if the amplitude is small enough, the nonlinear results are consistent with the linear results, demonstrating an alternative procedure for nonlinear analysis of SAW devices working in nonlinear state.

Molecular dynamics modeling of nonlinear propagation of surface acoustic waves

A new computational setup suitable for the exploration of nonlinear effects in free propagation and dissipation of surface acoustic waves (SAWs) is developed based on the molecular dynamics (MD) simulation method. First applications of the computational model demonstrate the ability of atomistic simulations to reproduce the key features of the nonlinear SAW evolution, which are distinct from their well-known counterparts in bulk wave propagation. In particular, the MD simulations predict the increasing localization of the acoustic energy near the surface of the substrate during the nonlinear sharpening of the wave profile, which leads to the formation of a shock front with characteristic cusps in the horizontal strain and velocity profiles. The peak values of surface strain and velocity associated with the cusps can significantly exceed those of the initial wave. Some of the effects revealed in the MD simulations are outside the capabilities of continuum-level models and have not been explored so far. These include the observation of an unusual quadratic correction to the dispersion relation at short wavelengths defined by the frequency-dependent localization of SAWs near the surface of the substrate, the establishment of a new mechanism of the energy dissipation at the SAW shock front, where SAW harmonics generated at the limit of frequency up-conversion transform very effectively into clouds of phonon wave packets descending into the substrate bulk, and the generation of localized zones of plastic deformation at a substantial distance from the wave source. Overall, the MD methodology developed for atomistic modeling of free SAW propagation not only enables detailed analysis of the intrinsic properties of nonlinear SAWs and verification of theoretical models but also opens up a broad range of opportunities for investigation of acoustically induced surface processes, material modification by SAWs, and the interaction of SAWs with preexisting crystal defects and other material heterogeneities.

(Invited) Heterogeneous Integration of Sub-Micron Thickness Epitaxial Ingaas(P) with Lithium Niobate for Active and Nonlinear Surface Acoustic Wave Devices

Radio frequency (RF) devices are becoming more multi-band, increasing the number of filters and other front-end components while simultaneously pushing towards reduced cost, size, weight, and power (CSWaP). One approach to reducing CSWaP is to eliminate high quality factor filtering that relies on acoustic wave technologies, allowing end-to-end solutions in CMOS or compound semiconductor platforms. Yet another way would be to augment the achievable functionalities of electromechanical/acoustic filtering chips to include “active” and nonlinear functionalities, such as gain and mixing. The acoustoelectric (AE) effect could enable such active acoustic wave devices, but, to compete with the performance of today’s multi-chip architectures, any solution to this problem needs to provide high gain, large bandwidth, low noise figure, and sufficient power handling, in addition to the reduced CSWaP. Surface acoustic wave (SAW) amplifiers based on the AE effect were demonstrated as early as the 1960s. In these devices, evanescent fields associated with piezoelectric acoustic waves interact with charge carriers undergoing voltage-induced drift. The interaction causes polarization of the drifting majority charge carriers that leads to a Coulomb drag effect, resulting in acoustic wave attenuation or amplification, analogous to a traveling-wave tube amplifier. The amplifier performance is improved by utilizing a piezoelectric substrate with a large electromechanical coupling coefficient, which alone determines the maximum gain, combined with an acoustically thin semiconductor with low conductivity and high mobility to lower the required voltage for a given gain. Previous demonstrations of SAW amplifiers have resulted in over 100 dB of RF output contrast (a.k.a. electronic gain), but at voltages exceeding 1 kV. Molecular beam epitaxy (MBE) and metal-organic chemical vapor deposition (MOCVD) were either in their infancy or not yet invented at the time, making it impossible to seamlessly integrate low defectivity, thin semiconductors with low conductivity and high mobility together with high electromechanical coupling coefficient piezoelectric substrates. Thus, previous AE amplifiers consisted of essentially one of two types: 1) evaporated thin semiconductor layers with large conductivity and high defectivity on piezoelectric substrates or 2) high quality bulk crystalline semiconductors separated from the piezoelectric by a thin air gap to prevent acoustic radiation into the thick semiconductor. The first approach yielded performance limited by the sub-optimal material properties; the second approach significantly reduced the AE interaction strength and made the devices more dispersive, which prevents high frequency operation. A third approach uses charge confinement structures or the high mobility of 2D materials, but performance of these devices has never approached that of the other two. Here, we present a high-gain leaky SAW (LSAW) amplifier based on heterogenous integration of an epitaxial III-V semiconductor and lithium niobate (LiNbO3), providing a solution to the aforementioned problems and enabling compact, high-gain devices with significantly lower power consumption. YX LiNbO3 is chosen due to its exceptionally high electromechanical coupling coefficient (~25%), providing the highest electromechanical coupling for a SAW on bulk LiNbO3. We demonstrate gain of 1.9 dB/Λ in a 338 μm long device, where Λ is the acoustic wavelength, equivalent to an electronic gain of 30.3 dB and a terminal gain of 5 dB. Moreover, on account of the directly bonded semiconductor layer’s low thickness and conductivity and relatively high gain, this large peak gain occurs at only -55 V.

Vector soliton of self-induced transparency of a generalized love wave

A theory of acoustic self-induced transparency of a two-component vector soliton for a generalized Love wave is constructed. The three-layer system contains a resonance transition layer with paramagnetic impurity atoms or quantum dots. It is shown that, under these conditions, a vector soliton of the generalized Love wave can be formed. It oscillates at the sum and difference frequencies in the vicinity of the carrier wave frequency. Explicit analytical expressions for the parameters of a nonlinear surface acoustic wave are presented. The parameters depend on the elastic properties of the contacting media, the resonance transition layer, and the transverse structure of the wave. Numerical calculations are carried out for the three-layer Al2O3/ZnO/SiO2 system. The significant difference between the two-component vector soliton and singlecomponent soliton is shown.

Resonance vector soliton of the Rayleigh wave.

A theory of acoustic vector solitons of self-induced transparency of the Rayleigh wave is constructed. A thin resonance transition layer on an elastic surface is considered using a model of a two-dimensional gas of impurity paramagnetic atoms or quantum dots. Explicit analytical expressions for the profile and parameters of the Rayleigh vector soliton with two different oscillation frequencies is obtained, as well as simulations of this nonlinear surface acoustic wave with realistic parameters, which can be used in acoustic experiments. It is shown that the properties of a surface vector soliton of the Rayleigh wave depend on the parameters of the resonance layer, the elastic medium, and the transverse structure of the surface acoustic wave.

Strong enhancement of surface diffusion by nonlinear surface acoustic waves

The phenomenon of acoustic activation of surface diffusion is investigated in a combined computational and experimental study. The ability of pulsed laser-generated surface acoustic waves (SAWs) to enhance the mobility of small atomic clusters is demonstrated by directly tracking, with fluorescence microscopy, individual $\mathrm{A}{\mathrm{u}}_{8}$ clusters moving on a (111) silicon substrate. A 19-fold increase in the effective diffusion coefficient is measured in room temperature experiments in the presence of SAWs generated by nanosecond pulse laser irradiation at a 100 Hz repetition rate. A strong enhancement of cluster mobility by SAWs is also observed in large-scale molecular dynamics simulations of surface diffusion of small atomic clusters. The analysis of the computational results demonstrates that the nonlinear sharpening of SAWs and the corresponding enrichment of the SAW spectra by high frequency harmonics which are capable of dynamic coupling to the cluster vibrations are responsible for the efficient acoustic activation of surface mobility in the simulations. The increase in the effective diffusion coefficient is proportional to the number of the SAW pulses passing through the diffusion region per unit time and a dramatic 4500-fold diffusion enhancement (corresponds to an equivalent temperature increase by $\ensuremath{\sim}{10}^{3}\phantom{\rule{0.16em}{0ex}}\mathrm{K}$) is predicted in the simulations for $15\phantom{\rule{0.16em}{0ex}}\mathrm{GHz}$ SAWs. The ability of SAWs to affect atomic-level surface processes has far-reaching implications for the design of new techniques where the acoustic energy serves as an effective substitution for thermal activation in applications where heating must be avoided or rapid switching of surface conditions is required.

Nonlinear surface acoustic waves on lithium niobate in microfluidic devices

Surface acoustic waves (SAW) are used frequently in microfluidic devices. Normally SAWs are generated on the surface of a piezoelectric material. Commonly used PZT is not appropriate for biomedical applications because of its high lead content, over 60% by weight. In this talk, a study of nonlinear SAW propagation in a piezoelectric substrate is presented. Model equations describing nonlinear SAW propagation in a piezoelectric crystal are derived from first principles. Elastic, piezoelectric, dielectric, and electrostrictive properties of a crystal with arbitrary symmetry are taken into account. The derived evolution equations are integrated numerically to illustrate nonlinear distortion of an initially sinusoidal wave of finite amplitude. As an example, SAW propagation along the X axis on single crystal 127.680 YX-cut lithium niobate (LiNbO3), referred to as 128-YX-LN, is considered. This LiNbO3 cut is typically used in microfluidic devices because it provides large mechanical displacements in the substrate. Analysis of the nonlinearity matrix permits quantification of the relative contributions to surface wave distortion from each physical phenomenon. [Work supported by the IR&D program at ARL:UT.]

Ferroelectric domain building blocks for photonic and nonlinear optical microstructures in LiNbO3

The ability to manipulate the size and depth of poling inhibited domains, which are produced by UV laser irradiation of the +z face of lithium niobate crystals followed by electric field poling, is demonstrated. It is shown that complex domain structures, much wider than the irradiating laser spot, can be obtained by partially overlapping the subsequent UV laser irradiated tracks. The result of this stitching process is one uniform domain without any remaining trace of its constituent components thus increasing dramatically the utility of this method for the fabrication of surface microstructures as well as periodic and aperiodic domain lattices for nonlinear optical and surface acoustic wave applications. Finally, the impact of multi exposure on the domain characteristics is also investigated indicating that some control over the domain depth can be attained.

The mechanical properties of various chemical vapor deposition diamond structures compared to the ideal single crystal

The structural and electronic properties of the diamond lattice, leading to its outstanding mechanical properties, are discussed. These include the highest elastic moduli and fracture strength of any known material. Its extreme hardness is strongly connected with the extreme shear modulus, which even exceeds the large bulk modulus, revealing that diamond is more resistant to shear deformation than to volume changes. These unique features protect the ideal diamond lattice also against mechanical failure and fracture. Besides fast heat conduction, the fast vibrational movement of carbon atoms results in an extreme speed of sound and propagation of crack tips with comparable velocity. The ideal mechanical properties are compared with those of real diamond films, plates, and crystals, such as ultrananocrystalline (UNC), nanocrystalline, microcrystalline, and homo- and heteroepitaxial single-crystal chemical vapor deposition (CVD) diamond, produced by metastable synthesis using CVD. Ultrasonic methods have played and continue to play a dominant role in the determination of the linear elastic properties, such as elastic moduli of crystals or the Young’s modulus of thin films with substantially varying impurity levels and morphologies. A surprising result of these extensive measurements is that even UNC diamond may approach the extreme Young’s modulus of single-crystal diamond under optimized deposition conditions. The physical reasons for why the stiffness often deviates by no more than a factor of two from the ideal value are discussed, keeping in mind the large variety of diamond materials grown by various deposition conditions. Diamond is also known for its extreme hardness and fracture strength, despite its brittle nature. However, even for the best natural and synthetic diamond crystals, the measured critical fracture stress is one to two orders of magnitude smaller than the ideal value obtained by ab initio calculations for the ideal cubic lattice. Currently, fracture is studied mainly by indentation or mechanical breaking of freestanding films, e.g., by bending or bursting. It is very difficult to study the fracture mechanism, discriminating between tensile, shear, and tearing stress components (mode I–III fracture) with these partly semiquantitative methods. A novel ultrasonic laser-based technique using short nonlinear surface acoustic wave pulses, developing shock fronts during propagation, has recently been employed to study mode-resolved fractures of single-crystal silicon. This method allows the generation of finite cracks and the evaluation of the fracture strength for well-defined crystallographic configurations. Laser ultrasonics reaches the critical stress at which real diamond fails and therefore can be employed as a new tool for mechanistic studies of the fracture behavior of CVD diamond in the future.

Estimation methodology for amplitude of second-order harmonic in nonlinear surface acoustic wave measured by optical diffraction method

An estimation methodology for amplitude from the fundamental to fourth-order harmonic composed of nonlinear surface acoustic waves on a LiNbO3 substrate with a 128° Y-X propagation axis was demonstrated. First, equations for estimation of amplitudes from diffracted light intensity were shown and then numerical simulations of main factors were carried out. Normalized diffraction light intensities due to components of nonlinear surface acoustic waves were measured and their amplitudes were obtained from measured values. Finally, the amplitude of the second harmonic propagating on a gold thin film of about 50 nm thickness was estimated. It was found that the amplitude of the second harmonic increased continuously from 0.8 to 2.0 A with propagation distance in the thin film.

Sizing of partially closed surface-breaking microcracks with broadband Rayleigh waves

Sizing of cracks in the range of tens of micrometers by laser-generated surface acoustic wave (SAW) pulses with a bandwidth of up to 200 MHz is reported. The radius of a semicircular surface-breaking crack was evaluated using two methods, one based on the experimentally measured reflection coefficient and the other on the frequency dependence of the phase lag of the transmitted wave. These quantities were also simulated numerically by means of the finite differences method and fitted to the experimental ones by varying the assumed size of the crack. In both cases the interaction between crack faces was taken into account by an effective interfacial stiffness parameter and the crack sizes obtained acoustically were compared with those measured by optical microscopy. Nondestructive evaluation was extended to the characterization of real microcracks in the range of tens of micrometers with the laser-based pump-probe technique. The microcracks studied were generated in fused silica by strongly nonlinear SAW pulses with shocks in a separate experiment.

Comparison of mode-resolved fracture strength of silicon with mixed-mode failure of diamond crystals

Currently ab initio theory provides the ideal tensile and shear strength of the {111} cleavage plane in single-crystal silicon and diamond only for few selected planes and directions (‘geometries’). These values can be compared with the real strength of nano-, micro-, and single-crystalline devices to roughly judge their mechanical quality. A novel contact-free and notch-free optical laser method allows the measurement of the fracture strength with plane nonlinear surface acoustic waves (SAWs), providing a unique way to discriminate between tensile and shear stresses for well-defined crystallographic planes and directions in anisotropic materials. Calibration yields the critical fracture stress or strength for the geometries, which can be compared with theory. In the case of diamond mostly mechanistically unresolved mixed-mode failure has been studied for complex geometries. Nevertheless, the comparison of these critical failure stresses with the strength of the ideal lattice and the mode- and geometry-resolved fracture behavior of silicon provides new insight into the mechanical stability and failure behavior of diamond materials.

3P3-12 Thickness Effect of Gold Film on Dynamics of Second Harmonic in Nonlinear Surface Acoustic Wave(Poster Session)

3P3-12 Thickness Effect of Gold Film on Dynamics of Second Harmonic in Nonlinear Surface Acoustic Wave(Poster Session)

Determination of linear and nonlinear mechanical properties of diamond by laser-based surface acoustic waves

The laser-based excitation of surface acoustic wave (SAW) narrowband trains and broadband pulses is described. SAW detection with a piezoelectric foil transducer was used to determine the Young's modulus of rough nano- and microcrystalline diamond films with linear SAWs. For high quality films ~ 1000 GPa is approached, near the stiffness of ideal polycrystalline diamond of 1143 GPa, indicating that this property is predominantly controlled by the diamond crystallites and not the grain boundaries. With strongly nonlinear SAW pulses developing shocks, fracture experiments were performed for well-defined crystallographic geometries of single-crystal silicon. The critical stresses of several gigapascals and strains of about 0.01 realized in these measurements are sufficient to determine the strength of nano- and microcrystalline diamond films, as well as natural single-crystal diamond. Their strength is one to two orders of magnitude smaller than the ideal tensile (shear) strength of 95 GPa (93 GPa), and thus reaches only several gigapascals, accessible by the pulsed SAW method. The surprisingly low strength of diamond materials indicates that the quality of the grain boundaries and defects plays an essential role in the fracture process.