Resonance ultrasound spectroscopy with laser-Doppler interferometry for studying elastic properties of thin films

We propose an advanced method to determine the elastic-stiffness coefficients Cij of thin films using resonance ultrasound spectroscopy (RUS). It uses free-vibration resonance frequencies of a film/substrate layered solid and derives inversely the film's Cij from the resonance frequencies. We develop a piezoelectric tripod consisting of two pinducers and one support to place the specimen on it and measure the resonance frequencies with high enough accuracy. Furthermore, we achieve mode identification by measuring deformation distributions on the vibrating specimen surface using laser-Doppler interferometry. Accurate measurements of frequencies and correct mode identification are the keys for deducing reliable Cij of the film. We applied this technique to copper thin films deposited of Si substrates. The resulting film's Cij are considerably smaller than the bulk's Cij and show anisotropy between the out-of-plane direction and in-plane direction.     

Determination of elastic moduli of rock samples using resonant ultrasound spectroscopy

Resonant ultrasound spectroscopy (RUS) is a method whereby the elastic tensor of a sample is extracted from a set of measured resonance frequencies. RUS has been used successfully to determine the elastic properties of single crystals and homogeneous samples. In this paper, we study the application of RUS to macroscopic samples of mesoscopically inhomogeneous materials, specifically rock. Particular attention is paid to five issues: the scale of mesoscopic inhomogeneity, imprecision in the figure of the sample, the effects of low Q, optimizing the data sets to extract the elastic tensor reliably, and sensitivity to anisotropy. Using modeling and empirical testing, we find that many of the difficulties associated with using RUS on mesoscopically inhomogeneous materials can be mitigated through the judicious choice of sample size and sample aspect ratio.     

Complete mode identification for resonance ultrasound spectroscopy

This study is devoted to deducing exact elastic constants of an anisotropic solid material without using any advance information on the elastic constants by incorporating a displacement-distribution measurement into resonant ultrasound spectroscopy (RUS). The usual RUS method measures free-vibration resonance frequencies of a solid and compares them with calculations to find the most suitable set of elastic constants by an inverse calculation. This comparison requires mode identification for the measured resonance frequencies, which has been difficult and never been free from ambiguity. This study then adopts a laser-Doppler interferometer to measure the displacement-distribution patterns on a surface of the vibrating specimen mounted on pinducers; comparison of the measured displacement distributions with those computed permits us to correctly identify the measured resonance frequencies, leading to unmistakable determination of elastic constants. Because the displacement patterns are hardly affected by the elastic constants, an exact answer is surely obtained even when unreasonable elastic constants are used as initial guesses at the beginning of the inverse calculation. The usefulness of the present technique is demonstrated with an aluminum alloy and a langasite crystal.     

Determination of elastic modulus of a beam by using electronic speckle pattern interferometry

This paper proposes a sonic resonance test for an elastic modulus measurement which is based on the electronic speckle pattern interferometry. Previous measurement technique of elastic constant has the limitation of application for thin film or polymer material because contact to specimen affects the result. It has been developed as a non-contact optical measurement technique which can visualize resonance vibration mode shapes with whole field. The maximum vibration amplitude at each vibration mode shape is a clue to find the resonance frequencies. The dynamic elastic constant of test material can be easily determined from vibration of a beam equation using the measured resonance frequencies. The proposed technique is able to give high accurate elastic modulus of materials through a simple experimental set-up and analysis. The experimental result also compared to the theoretical result.     

Resonant ultrasound spectroscopy and homogeneity in polycrystals

Resonant ultrasound spectroscopy (RUS) is capable of determining the bulk elastic properties of a solid from its characteristic vibration frequencies, given the dimensions, density and shape of the sample. The model used for extracting values of the elastic constants assumes perfect homogeneity, which can be approximated by average-isotropic polycrystals. This approximation is excellent in the small grain regime assumed for most averaging procedures, but for real samples with indeterminate grain size distributions, it is not clear where the approximation breaks down. RUS measurements were made on pure copper samples where the grain size distribution was changed by progressive heat treatments in order to find a quantitative limit for the loss of homogeneity. It is found that when a measure of the largest grains is 15% of the sample’s smallest dimension, the deviation in RUS fits indicates elastic inhomogeneity.     

Measuring elastic constants of arbitrarily shaped samples using resonant ultrasound spectroscopy

One of the most important undertakings for materials is the measurement of the elastic behavior. As derivatives of the free energy with respect to atomic displacements, the elastic properties are closely connected to the thermodynamic properties of the material. Elastic behavior is a sensitive probe of the lattice environment in which all solid state phenomena occur, particularly in the vicinity of a phase transition. A useful method for measuring elastic properties is resonant ultrasound spectroscopy (RUS). Some novel materials to which RUS might be applied are often fragile or chemically reactive so that they cannot be polished into the shapes required by conventional RUS; for such cases a finite element method may be used. In this paper a discussion and test of a finite element method for RUS with arbitrarily shaped samples is provided.     

Combining Brillouin spectroscopy and laser-SAW technique for elastic property characterization of thick DLC films

Surface Brillouin spectroscopy (SBS) has been widely used for elastic property characterization of thin films. For films thicker than 500 nm, however, the wavelength of surface acoustic wave in the frequency range available for SBS is smaller than film thickness, and the SBS measures only the Rayleigh wave of the film. The laser-SAW technique, on the other hand, measures only the low-frequency portion of the surface acoustic wave dispersion and can estimate only one elastic modulus of the film (typically Young's modulus). In this work, we have combined the two methods to determine both Young's modulus and Poisson's ratio of a diamond-like carbon (DLC) film. It was found that reasonable estimates can be obtained for the longitudinal wave velocity, shear wave velocity, and Young's modulus of the film. The Poisson's ratio, however, still has a relatively large measurement error.     

Elastic constants of natural quartz

The elastic constants of a natural-quartz sphere using resonance-ultrasound spectroscopy (RUS) are measured. The measurements of the near-traction-free vibrational frequencies of the sphere are matched with the predicted frequencies from the dynamic theory of elasticity, with optimized estimates for the elastic constants driving the differences between these sets of frequencies to a minimal value. The present computational model, although based on earlier approaches, is the first application of RUS to trigonal-symmetry spheres. Quartz shows six independent elastic constants, and our estimates of these constants are close to those computed by other means. Except for C14, after a 1% mass-density correction, natural quartz and cultured quartz show the same elastic constants. Natural quartz shows higher internal frictions.     

Effects of frequency/polarization allocations and the zero-dispersion frequency on FDM lightwave transmission systems

In long-haul frequency-division-multiplexing lightwave transmission systems, transmission characteristics are degraded by four-wave mixing (FWM) generated in optical fibers. To overcome this problem, several FWM suppression techniques have been reported. In this paper, dependence of FWM noises on frequency allocations, polarization allocations, and the zero-dispersion frequency is investigated. It is revealed that FWM noises are drastically decreased in frequency allocations such as equally spaced, repeated unequally spaced (RUS), equally spaced RUS, and unequally spaced RUS allocations by arranging polarization allocations of the channels with an increase in a separation between the channel frequencies and the zero-dispersion frequency.     

Influence of modulation formats on FWM noises in FDM optical fiber transmission systems

In long-haul frequency-division-multiplexing (FDM) lightwave transmission systems, transmission characteristics are degraded by four-wave mixing (FWM) in optical fibers. To overcome this problem in equally-spaced (ES) allocations, modified repeated unequally-spaced (RUS) allocations such as equally-spaced RUS (ERUS) and unequally-spaced RUS (URUS) allocations have been already examined.In this paper, we focus on the fact that FWM noises are closely related to modulation formats and frequency allocations. To reduce FWM noises in FDM optical fiber transmission systems, FWM noises are analyzed for ES, RUS, ERUS, and URUS with modulation formats such as non-return-to-zero (NRZ), random return-to-zero (RZ), differential phase-shift keying (DPSK), and bit-phase arranged RZ (BARZ). It is found that FWM noises are lowest in URUS with BARZ.     

Application of Brillouin scattering to the local anisotropy and birefringence measurements of thin layers

Brillouin scattering is an efficient nondestructive and noncontact measurement method to obtain the wave properties of thin layers at hypersonic frequencies. The reflection induced ThetaA (RIThetaA) scattering geometry enables the simultaneous measurement of the phonons, which propagate in each direction of wave vectors of q(Theta A) (propagation in the film plane) and q(180) (back scattering). Using this scattering geometry, we could observe the refractive indices and birefringence of the piezoelectric poly-vinylidene fluoride (PVDF) film as a function of temperature. By introducing the microscopic technique, the elastic anisotropy and refractive index measurements in the minute area of polycrystalline ZnO films were also performed.     

Optical multilayer post growth instabilities: Analyses of Gd2O3/SiO2 system in combination with scanning probe force spectroscopy

Post growth multilayer instabilities of a certain periodic Gd₂O₃/SiO₂ multilayer systems have been investigated using scanning probe force-distance spectroscopy and optical spectrophotometric techniques. In the present work, we have noticed a strong correlation between the force spectroscopic results and the spectral properties of multilayer thin films, although measurement techniques and operating principles are quite different. From the experimental analysis, it was quite evident that the instability process, which starts during the nucleation and growth stage in thin films, continues to persist at a much longer time scale under post growth conditions. During this study it has been noticed that the elastic properties of the constituent thin films, the layer geometry and the bilayer thickness have strong correlation in trickling the multilayer instabilities. Such aspects also have strong interconnections with the morphological and viscoelastic changes. It is also noticed that most of the instabilities results cannot only be explained through elastic nature of the material alone. Instead, total number of layers, the layer structures, morphological changes, corresponding stiffness and the adhesion properties of the multilayer contribute substantially to these phenomena.     

Application of digital speckle pattern interferometry and wavelet transform in measurement of transverse vibrations in square plate

In this paper the study of out-of-plane or transverse vibrations in a square plate using digital speckle pattern interferometry (DSPI) is presented. To improve the measurement accuracy, we have implemented a new filtering scheme based on combination of average/median filtering and Symlet wavelet filtering which enhances the signal to noise ratio in the speckle interferogram obtained from DSPI. A large number of fringe patterns are shown for square plate with two different boundary conditions. Experimentally obtained resonance frequencies for the square plate for the boundary condition one edge fixed and other edges being free, the resonance frequencies obtained from DSPI show good agreement with that obtained from classical theory for thin plates.     

Effect of argon ion activity on the properties of Y2O3 thin films deposited by low pressure PACVD

Yttrium oxide thin films are deposited by microwave electron cyclotron resonance (ECR) plasma assisted metal organic chemical vapour deposition process using an indegeneously developed Y(thd)₃ {(2,2,6,6-tetramethyl-3,5-heptanedionate)yttrium} precursor. Depositions were carried out at two different argon gas flow rates keeping precursor and oxygen gas flow rate constant. The deposited coatings are characterized by X-ray photoelectron spectroscopy (XPS), glancing angle X-ray diffraction (GIXRD) and infrared spectroscopy. Optical properties of the films are studied by spectroscopic ellipsometry. Hardness and elastic modulus of the films are measured by load depth sensing nanoindentation technique. Stability of the film and its adhesion with the substrate is inferred from the nanoscratch test.It is shown here that, the change in the argon gas flow rates changes the ionization of the gas in the microwave ECR plasma and imposes a drastic change in the characteristics like composition, structure as well as mechanical properties of the deposited film.     

Resonant ultrasound spectroscopy measurement of Young's modulus,shear modulus and Poisson's ratio as a function of porosity for alumina and hydroxyapatite

Modulus–porosity relationships are critical for engineered bone tissue scaffold materials such as hydroxyapatite (HA), where porosity is essential to biological function. Resonant ultrasound spectroscopy (RUS) measurements revealed that the Young's modulus, E, and shear modulus, G, of both alumina and HA decrease monotonically with increasing volume fraction porosity, P, for 0.06 < P < 0.39 (alumina) and 0.05 < P < 0.51 (HA). Although the elastic moduli of porous materials have been measured by a number of different ultrasonic resonance techniques (of which the RUS technique is one example) and over the last decade the elastic moduli of many solids have been measured by the RUS technique, this study is the first systematic RUS study of porous materials. Comparison of E versus P data for alumina (which has been studied extensively) with literature data from several measurement techniques indicates the RUS technique is effective for modulus–porosity measurements. Another key result is that although the HA specimens included in this study have a unimodal pore size distribution, the details of the decrease in E and G with increasing P agree well with literature data for HA with both unimodal and bimodal pore size distributions. In addition, Poisson's ratio exhibits a local minimum in the porosity range of 0.2 < P < 0.25 for both HA and alumina, which may be related to the pore morphology evolution during sintering.     

Analysis of the substrate effects of strain-hardening thin films on silicon under nanoindentation

Mechanical properties of thin films on substrates can be evaluated directly through nanoindentation. For a comprehensive study, thin films should be characterized via Young’s modulus, yield stress and strain-hardening exponent at constant temperature. In this paper, we evaluate these effects of thin films on silicon substrate through finite element analysis. Thin films, from soft to hard relative to the silicon substrate, are investigated in three categories: soft films on hard substrates, soft to hard films on no elastic mismatch substrates, and hard films on soft substrates. In addition to examining the load-displacement curve, the normalized hardness versus normalized indentation depth is checked as well to characterize its substrate effect. We found that the intrinsic film hardness can be acquired with indentation depths of less than 12% and 20% of their film thickness for soft films on hard substrates and for soft to hard films on no elastic mismatch substrates, respectively. Nevertheless, nanoindentation of hard films on soft substrates cannot determine the intrinsic film hardness due to the fact that a soft substrate cannot support a hard film. By examining the von Mises stresses, we discovered a significant bending phenomenon in the hard film on the soft substrate. PACS 61.43.Bn; 62.20.-x; 68.03.Hj; 68.05.Cf; 68.08.De     

The use of piezoelectric film and ultrasound resonance to determine the complete elastic tensor in one measurement.

The ultrasonic and elastic properties of materials are conventionally measured using quartz, lithium niobate, etc., transducers and a pulse-echo technique with the transducer driven at resonance. Problems with the technique include transducer ringing, transducer-sample coupling, parallelism of sample faces, beam diffraction, and the necessity of remounting transducers in order to measure all of the elastic constants. Usually, these problems can be minimized, but with samples that are only a fraction of a millimeter in size, conventional ultrasound measurements become difficult if not impossible. However, nearly all of these problems may be avoided if a resonance technique is used, and all of the elastic constants may be determined with a single measurement. For the broadband response and minimum transducer loading required for a resonance measurement in a small sample, polyvinylidene fluoride (PVDF) piezoelectric film (as thin as 9 microns) is ideally suitable.     

Bulk-wave and guided-wave photoacoustic evaluation of the mechanical properties of aluminum/silicon nitride double-layer thin films

The development of devices made of micro- and nano-structured thin film materials has resulted in the need for advanced measurement techniques to characterize their mechanical properties. Photoacoustic techniques, which use pulsed laser irradiation to nondestructively induce very high frequency ultrasound in a test object via rapid thermal expansion, are suitable for nondestructive and non-contact evaluation of thin films. In this paper, we compare two photoacoustic techniques to characterize the mechanical parameters of edge-supported aluminum and silicon nitride double-layer thin films. The elastic properties and residual stresses in such films affect their mechanical performance. In a first set of experiments, a femtosecond transient pump–probe technique is used to investigate the Young’s moduli of the aluminum and silicon nitride layers by launching ultra-high frequency bulk acoustic waves in the films. The measured transient signals are compared with simulated transient thermoelastic signals in multi-layer structures, and the elastic moduli are determined. Independent pump–probe tests on silicon substrate-supported region and unsupported region are in good agreement. In a second set of experiments, dispersion curves of the A₀ mode of the Lamb waves that propagate along the unsupported films are measured using a broadband photoacoustic guided-wave method. The residual stresses and flexural rigidities for the same set of double-layer membranes are determined from these dispersion curves. Comparisons of the results obtained by the two photoacoustic techniques are made and discussed.     

Rapid determination of surface roughness of polycrystalline silicon following frontside and backside excimer laser irradiation

Excimer-laser crystallization (ELC) is the most commonly employed technology for fabricating low-temperature polycrystalline silicon (LTPS). Investigations on the surface roughness of polycrystalline silicon (poly-Si) thin films have become an important issue because the surface roughness of poly-Si thin films is widely believed to be related to its electrical characteristics. In this study, we develop a simple optical measurement system for rapid surface roughness measurements of poly-Si thin films fabricated by frontside ELC and backside ELC. We find that the incident angle of 20° is a good candidate for measuring the surface roughness of poly-Si thin films. The surface roughness of polycrystalline silicon thin films can be determined rapidly from the reflected peak power density measured by the optical system developed using the prediction equation. The maximum measurement error rate of the optical measurement system developed is less than 9.71%. The savings in measurement time of the surface roughness of poly-Si thin films is up to 83%. The method of backside ELC is suggested for batch production of low-temperature polycrystalline silicon thin-film transistors due to the lower surface roughness of poly-Si films and higher laser-beam utilization efficiency.     

Effect of strain relaxation of oxidation-treated SiGe epitaxial thin films and its nanomechanical characteristics

In this study, we examined the effect of high-temperature oxidation treatment on the SiGe epitaxial thin films deposited on Si substrates. The X-ray diffraction (XRD), atomic force microscopy (AFM), and nanoindentation techniques were employed to investigate the crystallographic structure, surface roughness, and hardness (H) of the SiGe thin films, respectively. The high-temperature oxidation treatment led to Ge pileup at the surface of the SiGe thin films. In addition, strain relaxation occurred through the propagation of misfit dislocations and could be observed through the cross-hatch pattern (800-900 °C) and SiGe islands (1000 °C) at the surface of the SiGe thin films. Subsequent hardness (H) measurement on the SiGe thin films by continuous penetration depth method indicated that the phenomenon of Ge pileup caused a slightly reduced H (below 50 nm penetration depth), while relaxation-induced defects caused an enhanced H (above 50 nm penetration depth). This reveals the influence of composition and defects on the structure strength of high-temperature oxidation-treated SiGe thin films.