Dispersion Curves Of Surface Acoustic Waves Research Articles

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.

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.

Study on the interfacial adhesion property of low-k thin film by the surface acoustic waves with cohesive zone model

The cohesive zone model being increasingly used in discrete fracture processes simulation is adopted to study the interfacial adhesion property of low dielectric constant film deposited on the silicon substrate in this work. The two parameters, maximum normal traction and normal interface characteristic length in cohesive zone model, are taken into account to calculate the theoretical surface acoustic wave dispersion curves. Broadband surface acoustic wave signals with effective frequency up to 200MHz are generated by short pulse ultraviolet laser source and detected by a piezoelectric transducer. The interfacial adhesion properties of dense and porous films determined accurately by matching the experimental dispersion curves with the calculated theoretical dispersion curves are 10.7PPa/m and 2.8PPa/m, respectively. The results show that the adhesion quality of dense low dielectric constant film is better than that of the porous. The study exhibits that the adhesion properties determined by improved laser-generated surface acoustic wave technique have the same trends with the test results of the nanoscratch technique, which indicates that the surface acoustic wave technique with cohesive zone model is a promising and nondestructive method for determining interfacial adhesion properties between low dielectric constant film and substrate.

Determination of thermoelastic material properties by differential heterodyne detection of impulsive stimulated thermal scattering

The underlying working principle of detecting impulsive stimulated scattering signals in a differential configuration of heterodyne diffraction detection is unraveled by involving optical scattering theory. The feasibility of the method for the thermoelastic characterization of coating-substrate systems is demonstrated on the basis of simulated data containing typical levels of noise. Besides the classical analysis of the photoacoustic part of the signals, which involves fitting surface acoustic wave dispersion curves, the photothermal part of the signals is analyzed by introducing thermal wave dispersion curves to represent and interpret their grating wavelength dependence. The intrinsic possibilities and limitations of both inverse problems are quantified by making use of least and most squares analysis.

Study of surface acoustic waves in SiO2/LiNbO3 layered-structure phononic crystals

Phononic crystal (PnC) in half-space allows anisotropic propagation and band gaps for surface acoustic wave (SAW) and promise applications such as filters and reflectors. For the feasible MEMS fabrication, a PnC comprised of cylindrical holes in a SiO2 layer covering a LiNbO3 substrate was proposed and analyzed numerically. Dispersion curves of SAWs in the PnC were calculated by using finite element method and then the band gap range for SAW was indicated. The variation of band gaps by modifying the layer thickness and cylinder size was reported. Simulation shows that SAW propagation could be stopped by thirty rows of PnCs. Then reflective gratings and resonant cavities for SAW were designed accordingly. The result showed feasibility of applying PnC in acoustic electronics devices.

Experimental and numerical studies for nondestructive evaluation of human enamel using laser ultrasonic technique

In this paper, a nondestructive laser ultrasonic technique is used to generate and detect broadband surface acoustic waves (SAWs) on human teeth with different demineralization treatment. A scanning laser line-source technique is used to generate a series of SAW signals for obtaining the dispersion spectrum through a two-dimensional fast Fourier translation method. The experimental dispersion curves of SAWs are studied for evaluating the elastic properties of the sound tooth and carious tooth. The propagation and dispersion of SAWs in human teeth are also been studied using the finite element method. Results from numerical simulation and experiment are compared and discussed, and the elastic properties of teeth with different conditions are evaluated by combining the simulation and experimental results.

Nondestructive determination of interfacial adhesion property of low-k/Si by the surface acoustic waves

Nondestructive surface acoustic wave (SAW) technique promoted for interfacial adhesion investigation is employed to study the adhesion properties of both the porous and the dense low dielectric constant (low-k) films deposited on the silicon substrate. Spring boundary model is employed by introducing the parameters of distributed shear and normal spring constant per unit area (KT and KN) between the film and the substrate to take the adhesion property into account to calculate the theoretical SAW dispersion curves. Broadband SAW signals are generated by short pulse ultraviolet laser source and detected by a piezoelectric transducer. Interfacial adhesion properties of the low-k samples can be obtained by fitting the experimental dispersion curve with the theoretical ones. The smooth experimental dispersion curves with maximum frequency up to 150 and 200MHz are achieved for the porous and dense low-k samples, respectively. The determination result indicates that the adhesion property of dense low-k film is much better than that of the porous low-k sample used in this study. The determined adhesion result by SAW exhibits the same trend with the test of the nanoscratch.

Laser‐generated surface acoustic waves in copper line arrays on silicon

Laser‐generated acoustics waves are widely used to control the fabrication on metal interconnect structures in the semiconductor industry. On the other hand, acoustic properties of such structures, typically comprised of periodic arrays of metal lines embedded in a dielectric film on a silicon substrate, pose some interesting wave propagation problems. We will report measurements of surface acoustic waves (SAWs) performed using laser‐induced transient grating technique on periodic arrays of micron‐wide copper lines. As expected, SAW dispersion curves yield small band gaps at the Brillouin zone boundary. However, much larger band gaps are observed within the 1st Brillouin zone. We believe that these giant band gaps are formed due to avoided crossing of the 1st and 2nd order surface acoustic modes of the film/substrate structure when the 1st mode dispersion curve becomes folded due to periodicity. Another observed phenomenon is a spectacularly sharp increase in the acoustic attenuation occurring when the folded surface mode becomes coupled to a bulk wave.

激光冲击硬化材料中的声表面波

Laser shock peening is a well-known method for extending the fatigue life of metal components by introducing near-surface compressive residual stress. The surface acoustic waves (SAWs) are dispersive when the near-surface properties of materials are changed. So the near-surface properties (such as the thickness of hardened layers, elastic properties, residual stresses, etc.) can be analyzed by the phase velocity dispersion. To study the propagation of SAWs in metal samples after peening, a more reasonable experimental method of broadband excitation and reception is introduced. The ultrasonic signals are excited by laser and received by polyvinylindene fluoride (PVDF) transducer. The SAW signals in aluminum alloy materials with different impact times by laser shock peening are detected. Signal spectrum and phase velocity dispersion curves of SAWs are analyzed. Moreover, reasons for dispersion are discussed.

Surface acoustic wave depth profiling of a functionally graded material

The potential and limitations of Rayleigh wave spectroscopy to characterize the elastic depth profile of heterogeneous functional gradient materials are investigated by comparing simulations of the surface acoustic wave dispersion curves of different profile-spectrum pairs. This inverse problem is shown to be quite ill posed. The method is then applied to extract information on the depth structure of a glass-ceramic (alumina) functionally graded material from experimental data. The surface acoustic wave analysis suggests the presence of a uniform coating region consisting of a mixture of Al2O3 and glass, with a sharp transition between the coating and the substrate. This is confirmed by scanning electron microscope with energy dispersive x-ray analysis.

The determination for the adhesion of film and substrate by surface acoustic waves

Layered film structures are widely applied in industry. The adhesion of thin film, which controls the product quality, is a key factor to be known before being used. The possibility of applying the surface acoustic waves (SAWs) technique to determine the adhesion of film and substrate is explored by a theoretical approach. The adhesion of interface is modeled by a spring boundary model. A commonly used structure of low- k film deposited on Si substrate in semiconductor industry is taken as an example. Theoretical results show that the SAWs dispersion curves are well separated for the distributed spring constants from 0.05 TPa to 5 TPa, which correspond to the poorly bonded and perfectly bonded interface, respectively. The results confirm that the SAWs technique has a high resolution on determining the adhesion property of film and substrate nondestructively.

Influence of oxygen on the elastic properties of nanocrystalline diamond films studied by laser-induced surface acoustic waves

Laser-induced surface acoustic waves (SAWs) were used to study the influence of oxygen on the elastic properties of nanocrystalline diamond films. A series of samples was grown by chemical vapor deposition (CVD) on the (1 0 0) plane of p-type silicon for 3 h under different O 2/(CH 4 + H 2) flow ratios from 0% to 8%. The elastic properties of these nanocrystalline diamond films were determined from the SAW dispersion curves. The maximum frequency realized was about 310 MHz in wideband SAW experiments and about 700 MHz using a narrowband mask method with several higher harmonics. It was found that the densities of all samples were surprisingly high, approaching the ideal value of diamond, whereas the Young’s modulus increased from 700 to 950 GPa with the addition of oxygen. It is concluded that oxygen has a significant positive effect on the elastic properties of nanocrystalline diamond.

Anisotropic Elastic Properties of Low-k Dielectric Materials

AbstractA non-contact optical technique based on laser-generated surface acoustic waves (SAWs) was used to characterize elastic properties of two types of thin (150-1100 nm) low-k films: more traditional non-porous organosilicate glass PECVD films (k=3.0) and novel mesoporous silica films fabricated in supercritical CO2 (k=2.2). The acoustic response of the non-porous samples is well described by a model of an elastically isotropic material with two elastic constants, Young's modulus and Poisson's ratio. Both parameters can be determined by analyzing SAW dispersion curves. However, the isotropic model fails to describe the SAW dispersion in the mesoporous samples. Modifying the model to allow a difference between in-plane and out-of plane properties (i.e., a transversely isotropic material) results in good agreement between the measurements and the model. The in-plane compressional modulus is found to be 2-3 times larger than the out-of plane modulus, possibly due to the anisotropic shape of the pores. Elastic anisotropy should therefore be taken into account in modeling mechanical behavior of low-k materials.

Modeling of surface acoustic waves in thin film stacks with an arbitrary number of layers (abstract)

An efficient mathematical algorithm for the analysis of surface acoustic waves (SAW) measurements in multilayered thin film stacks has been developed. It allows for a fast and accurate calculation of SAW velocities in stacks composed of an arbitrary number of layers with varying material properties and thicknesses. The inversion algorithm also enables fast determination of multiple stack parameters from SAW dispersion curves. The model is used in a semiconductor metrology tool designed for quality control in the manufacturing of integrated circuits. Surface acoustic waves are described by a special class of solutions of the wave equation satisfying specific boundary conditions at the surface of the media in which they propagate. In the case of a stack composed of thin films, the boundary conditions at the surface of the top layer correspond to a free surface (no stress), at the interface of the individual layers a continuity of both stress and displacement is imposed. In the case of isotropic media, or in certain cases when the wave propagates along planes of symmetry [e.g., (1,0,0) plane of a cubic crystal], the set of boundary conditions results in a system of 4N coupled linear equations for the stress and displacements, where N is the number of layers in the stack. For stacks with a large number of layers, the problem quickly becomes numerically challenging. Requirements imposed by the manufacturing process on the time for data analysis and for processing of the information require fast algorithms. Such an algorithm has been developed and is being implemented in the software to be used in in-line optoacoustic metrology systems. The algorithm is based on the concept of a response function. This function describes the response of an elastic medium to a periodic excitation on its surface. By using the response function the problem of solving a system of 4N linear algebraic equations is reduced to (N−1) matrix multiplications of 4×4 matrices and solving a 2×2 equation. In the application for which this algorithm was developed a laser beam split by a diffraction grating and projected on the surface of the stack produces the excitation of the SAW. The algorithm allows a user to analyze SAW data for a system of an arbitrary large number of layers that can be either elastically isotropic or anisotropic. It significantly accelerates the computation of SAWs, which is of prime importance for industrial applications.

SURFACE ACOUSTIC WAVE DETERMINATION OF SUBSURFACE STRUCTURE

Abstract Surface acoustic wave dispersion curves were used to nondestructively estimate properly profiles in three industrially significant material systems; electrodeposited nickel on copper, induction hardened steel, and a nickel-copper-nickel sandwich. The estimation requires that an inverse problem be solved for measured dispersion data. To study the mathematical approach, simulated dispersion data were used to examine solution uniqueness, required computational time and data measurement accuracy. The results show that a fast, robust and unique estimate of industrial subsurface structures can be made as long as an a priori set of parametric relationships is established which span the possible configurations to be measured and constrain the problem. Under these conditions measured dispersion data were used to nondestructively predict the underlying material property profiles to within good agreement of their destructively measured values.

Acoustic-microscopy measurements of the elastic properties of TiN/(VxNb1-x)N superlattices.

The elastic constants of (${\mathrm{V}}_{0.6}$${\mathrm{Nb}}_{0.4}$)N and (${\mathrm{V}}_{0.3}$${\mathrm{Nb}}_{0.7}$)N films have been determined from anisotropic surface acoustic wave (SAW) dispersion data measured by line-focus acoustic microscopy. Using the acoustic microscope, measurements of SAW velocities have also been carried out on the TiN/(${\mathrm{V}}_{0.6}$${\mathrm{Nb}}_{0.4}$)N (001) and TiN/(${\mathrm{V}}_{0.3}$${\mathrm{Nb}}_{0.7}$)N (001) and (111) superlattice films, all grown on cubic-crystalline MgO substrates. The phase velocities, measured as functions of the angle of propagation, display the expected anisotropic natures of (001) and (111) cubic symmetries. Dispersion curves of SAW's propagating along the symmetry axes have been obtained by measuring wave velocities for various film thicknesses and frequencies. From the elastic constants of homogeneous TiN, (${\mathrm{V}}_{0.6}$${\mathrm{Nb}}_{0.4}$)N, and (${\mathrm{V}}_{0.3}$${\mathrm{Nb}}_{0.7}$)N films, the effective elastic constants of TiN/(${\mathrm{V}}_{0.6}$${\mathrm{Nb}}_{0.4}$)N and TiN/(${\mathrm{V}}_{0.3}$${\mathrm{Nb}}_{0.7}$)N superlattice films and the corresponding phase velocities of SAW's have been calculated. The calculated dispersion curves show very good agreement with the experimental results. The dependence of the elastic properties of the superlattices on the TiN fraction, on the superlattice period, and on the crystallographic orientation has been investigated. The results show no elastic anomalies within measurement errors, indicating that previously reported hardness enhancements were not related to elastic property changes.

Elastic constants of single-crystal transition-metal nitride films measured by line-focus acoustic microscopy

The elastic constants of single-crystal NbN, VN, and TiN films were determined from surface acoustic wave (SAW) dispersion curves obtained by the use of an acoustic microscope with a line-focus beam. Measurements were carried out for single-crystal nitride films grown on the (001) plane of single-crystal cubic-symmetric MgO substrates. The phase velocities measured as functions of the angle of propagation display the expected anisotropy. Dispersion curves of SAWs propagating along the symmetry axes were obtained by measuring the wave velocities for various film thicknesses and frequencies. Using a modified simplex method, an inversion of the SAW dispersion data yielded the elastic constants of cubic symmetry, namely c11, c12, and c44. The Rayleigh surface wave velocities calculated from the determined elastic constants and known mass densities agree well with a result measured by Brillouin scattering spectroscopy reported elsewhere.

Effective elastic constants and acoustic properties of single-crystal TiN/NbN superlattices

Using the measured elastic constants of TiN and NbN single crystals with cubic symmetry, the effective elastic constants of single-crystal TiN/NbN superlattice films with tetragonal symmetry, namely c11, c12, c13, c33, c44, and c66 have been calculated for various thickness ratios of the layers. Using a line-focus acoustic microscope, measurements of surface acoustic waves (SAWs) have been carried out on single-crystal TiN/NbN superlattice films grown on the (001) plane of cubic crystal MgO substrates. The phase velocities measured as functions of the angle of propagation display the expected anisotropic nature of cubic crystals. Dispersion curves of SAWs propagating along the symmetry axes have been obtained by measuring wave velocities for various film thicknesses and frequencies. The SAW dispersion curves calculated from the effectiveelastic constants and the effective mass density of the superlattice films show very good agreement with experimental results. The results of this paper exhibit no anomalous dependence of the elastic constants on the superlattice period of TiN/NbN superlattices.