Elastic Constants Of Thin Films Research Articles

Picosecond Ultrasonics for Studying Elastic Modulus of Polycrystalline Chromium Nanofilms: Thickness Dependence and Stiffness Enhancement

Accurate measurement of elastic constants in thin films is still an important issue to understand the scale behavior of nanosized materials. In the present study, we introduced an advanced non-destructive method, picosecond ultrasonics (PU), for measuring the out-of-plane elastic modulus of thin chromium (Cr) films. The femtosecond light pulse is focused on the Cr film to excite the longitudinal acoustic phonons (LAP), which propagate along the thickness direction and repeat reflections inside the Cr film. Then, the propagation/distribution of LAP is detected by the time-delayed probe light pulse through the photoelastic effect. Therefore, we can determine the out-of-plane modulus by measuring the periodic pulse echoes or the breathing mode vibrations within the Cr film. For most Cr films, the determined modulus is smaller than the corresponding bulk value and decreases with the decreasing thickness, while for some Cr films, it closes and may exceed the bulk value. This work describes the thickness-dependent elasticity of thin Cr films and provides evidence of the stiffness enhancement in Cr films on the Si substrate. In addition, since LAP with central frequency up to 310 GHz is excited in Cr films on the SiO2 substrate, we also demonstrate the potential of Cr films as high-frequency photoacoustic transducers.

Measurement of elastic constants of thin films by hypersound: Picosecond ultrasound spectroscopy

Measurement of elastic constants of thin films by hypersound: Picosecond ultrasound spectroscopy

Properties of Thin Films of Barium–Strontium Titanate Solid Solutions by Induced Piezoelectric Effect

Piezoelectric effect equations have been derived by linearizing the nonlinear equations of state of a thin film existing in a paraelectric phase in the presence of an external electrical field (induced piezoelectric effect). The behavior of the piezoelectric and elastic constants of thin films of a solid barium–strontium titanate solution BST065 (x = 0.65) in a planar field at different misfit strain values has been studied numerically.

Surface Brillouin scattering observation of higher order resonances in annealed, ion-implanted CVD diamond

The phase velocity of Surface Acoustic waves exhibits no dispersion in homogeneous materials. However, normal or anomalous dispersion takes place in layered systems. This dispersion effect has been used to determine the elastic constants of thin films. However, gradients in materials properties in the near surface region lead to dispersion effects also and therefore can be easily detected by surface acoustic waves (SAWs). We have used this technique to study changes in shear elastic constants of diamond irradiated with carbon ions in the energy range typically used in doping semiconductor materials. The range of the radiation damage extends from the surface to a depth of ≈0.3 μm. The fluence used for implantation was chosen so that the damaged diamond layer would not reform after thermal annealing at ambient pressure. In this study we generated and detected SAWs on the implanted and annealed diamond face after deposition of a very thin Pt film of thickness of ≈20nm to enhance surface reflectivity. With increasing dispersion (k∥d), the Rayleigh wave velocity falls gradually from that of crystalline diamond to that of annealed amorphous layer. At critical values of product of parallel wave vector and film thickness (k∥d), Sezawa modes split off from the bulk wave threshold of the substrate (transonic state). These are guided modes with the displacement field having an oscillating component in the layer, and falling off exponentially in the substrate. In combination with the velocity of the longitudinal bulk waves, the Poisson ratio and Young's modulus of the implanted region were calculated.

Study on Young's modulus of thin films on Kapton by microtensile testing combined with dual DIC system

In this paper, a method is proposed to determine the in-plane elastic modulus of thin films. Thanks to our custom-designed dual digital image correlation (DIC) system, it is possible to measure the time-resolved strain of film and substrate simultaneously during the microtensile testing. The macroscopic strain difference between coated and uncoated section allows extracting the elastic constants of thin films with high precision. In the case of 400nm tungsten films coated on each side of one substrate over half of the gauge length, the value obtained agrees well with the bulk one. Furthermore, finite element method (FEM) has been performed to simulate the mechanical behavior of the specimen. High consistency with theoretical and experimental results is verified.

Influence of surface stresses on indentation response

Surface stresses lead to an effective change in the elastic constants of thin films and at surfaces. The development of modern scanning probe techniques like contact resonance atomic force microscopy empowers the experimenter to measure at scales where these effects become increasingly relevant. In this paper we employ a computational multiscale approach where we compare density functional theory (DFT) and molecular dynamics simulations as tools to calculate the thin-film/surface elastic behavior for silicon and strontiumtitanate. From the surface elastic constants gained by DFT calculations we develop a continuum finite-element multilayer model to study the impact of surface stresses on indentation experiments. In general the stress field of an indenter and thus the impact of surface stresses on the indentation modulus depends on its contact radius and on its particular shape. We propose an analytical model that describes the behavior of the indentation modulus as a function of the contact radius. We show that this model fits well to simulation results gained for a spherical and a flat punch indenter. Our results demonstrate a surface-stress-induced reduction of the indentation modulus of about 5% for strontiumtitanate and 6% for silicon for a contact radius of , irrespective of the indenter shape.

Poisson Ratio of Epitaxial Germanium Films Grown on Silicon

An accurate knowledge of elastic constants of thin films is important in understanding the effect of strain on material properties. We have used residual thermal strain to measure the Poisson ratio of Ge films grown on Si ⟨001⟩ substrates, using the sin2ψ method and high-resolution x-ray diffraction. The Poisson ratio of the Ge films was measured to be 0.25, compared with the bulk value of 0.27. Our study indicates that use of Poisson ratio instead of bulk compliance values yields a more accurate description of the state of in-plane strain present in the film.

On the possibility of direct determination of elastic constants of thin films in the transverse direction to the film plane

The possibility of determining the elastic constants of thin films deposited on the free end of an acoustic line in the transverse direction to the film plane is discussed. The proposed technique is based on measurement of changes in eigenfrequencies of a composite acoustic resonator composed of an acoustic line and an electroacoustic transducer of bulk acoustic waves upon its loading with a thin-film coating. Results of experimental verification of the proposed technique for a thin (3.25 μm) film of DST-30 rubber deposited on the free end of a resonator made of fused quartz with an operating range of 80–150 MHz are described. It is shown that the elasticity of a divinyl styrene rubber film lengthwise and crosswise its plane differs by almost four orders of magnitude.

MEASUREMENT OF YOUNG'S MODULUS AND POISSON'S RATIO OF THIN FILMS BY SYNCHROTRON X-RAY DIFFRACTION

A new experimental method for determining elastic constants of thin films is proposed. The curvatures of the single crystal substrates before and after depositing thin film are first measured using high-resolution X-ray rocking curve technique with high quality monochromatic and high intensity synchrotron radiation. The residual stress in the film is then calculated from the change in substrate curvature based on the well-known modified Stoney's equation. The formulae for calculating thin film's Young's modulus and Poisson's ratio are deduced based on measured residual stress and the lattice spacing dψ versus sin2ψ curves of the film before and after an unknown mechanical loading. LaNiO3 film grown on single crystal silicon substrate using pulsed laser deposition is employed to demonstrate the measurement method.

A Novel Technique to Determine Elastic Constants of Thin Films

AbstractA new X-ray diffraction technique to determine elastic moduli of polycrystalline thin films deposited on monocrystalline substrates is demonstrated. The technique is based on the combination of sin2ψ and X-ray diffraction wafer curvature techniques which are used to characterize X-ray elastic strains and macroscopic stress in thin film. The strain measurements must be performed for various hkl reflections. The stresses are determined from the substrate curvature applying the Stoney's equation. The stress and strain values are used to calculate hkl reflection dependent X-ray elastic moduli. The mechanical elastic moduli can be then extrapolated from X-ray elastic moduli considering film macroscopic elastic anisotropy. The derived approach shows for which reflection and corresponding value of the X-ray anisotropic factor Γ the X-ray elastic moduli are equal to their mechanical counterparts in the case of fibre textured cubic polycrystalline aggregates. The approach is independent of the crystal elastic anisotropy and depends on the fibre texture type, the texture sharpness, the amount of randomly oriented crystallites and on the supposed grain interaction model. The new method is demonstrated on a fiber textured Cu thin film deposited on monocrystalline Si(100) substrate. The advantage of the new technique remains in the fact that moduli are determined non-destructively, using a static diffraction experiment and represent volume averaged quantities.

Advanced resonant ultrasound spectroscopy for measuring anisotropic elastic constants of thin films

ABSTRACTThis paper presents an advanced resonant ultrasound spectroscopy (RUS) method to determine the elastic constants Cij of thin films. Polycrystalline thin films often exhibit elastic anisotropy between the film growth direction and the in‐plane direction, and they macroscopically show five independent elastic constants. Because all of the Cij of a deposited thin film affect the mechanical resonance frequencies of the film/substrate layer specimen, measuring resonance frequencies enables one to determine the Cij of the film with known density, dimensions and the Cij of the substrate. Resonance frequencies have to be measured accurately because of low sensitivity of the Cij of films to them. We achieved this by a piezoelectric tripod. Mode identification has to be made unambiguously. We made this measuring displacement–amplitude distributions on the resonated specimen surface by laser Doppler interferometry. We applied our technique to copper thin film and diamond thin film. They show elastic anisotropy and the Cij smaller than bulk values of Cij. Micromechanics calculations indicate the presence of incohesive bonded regions.

A method for calculating surface stress and surface elastic constants by molecular dynamics: application to the surface of crystal and amorphous silicon

For nano-scale thin film, effects of surface and interface, which can be ignored on a macroscale, become important. For example, surface energy and surface stress are key parameters for predicting the intrinsic stress of thin films. Several researchers have reported that the elastic constants of thin films are different from those of bulks. We have recently proposed new definitions and calculation methods regarding surface stress and elastic constants for thin films by extending Martin's method, which is useful for obtaining internal displacement and elastic constants within the framework of the molecular dynamics (MD) method. We applied our method to nano-scale thin films of crystal and amorphous silicon. It is found that elastic constants of thin film depend on both the surface elastic constants and on film thickness. Those values are significantly affected by the surface reconstructions. The width of the surface and the limit of continuum homogeneous approximation are also investigated.

Resonance Ultrasound Spectroscopy for Measuring Elastic Constants of Thin Films

We show an advanced technique for measuring elastic constants Cij of thin films deposited on substrates. Thin films often show anisotropy between the in-plane and out-of-plane directions because of their columnar structure, residual stress, texture, and incohesive bond. Then, thin films show macroscopically transverse isotropy and have five independent Cij. All the film Cij affect free-vibration resonance frequencies of the film/substrate layered specimen. Therefore, measuring the resonance frequencies permits us to determine the thin-film Cij with the other known parameters. In order to yield reliable Cij of thin films, we have to measure the resonance frequencies with sufficient accuracy and identify vibration modes of the measured resonance frequencies. We overcome these problems by developing a tripod and using a laser-Doppler interferometer, respectively. We applied the present technique to a copper thin film. Measured Cij are smaller than those of bulk and show elastic anisotropy. We attribute these features to the incohesive bond regions.

712 共振/レーザー法による薄膜の弾性定数測定と内部組織のマイクロメカニックス評価(GS-3 超音波計測)

We originally develop a measurement method for determining anisotropic elastic constants of thin films on substrates. It uses free-vibration resonance frequencies of a film/substrate rectangular parallelepiped specimen, which depend on dimensions, mass density and elastic constants of the film and substrate; film's elastic constants are inversely determined from the resonance frequencies. We measure the resonance frequencies with a high accuracy using a piezoelectric tripod transducer, consisting of needle-type transducers for generation and detection of vibration. Detected resonance peaks are identified by measuring the displacement distribution on the vibrating surface using laser-Doppler interferometer. We applied this method to copper and CVD diamond thin films. Their elastic constants show elastic anisotropy between the in-plane and out-of-plane directions. We attribute it to incohesive bonds at grain boundaries. This view is supported by micromechanics calculations.

Elastic constants of chemical-vapor-deposition diamond thin films: resonance ultrasound spectroscopy with laser-Doppler interferometry

Polycrystalline thin films show transverse isotropy (or hexagonal symmetry) and show five independent elastic constants because of columnar structure, texture, residual stress, and local incohesive bonds (or microcracks). In this paper, we developed an advanced method for measuring the anisotropic elastic constants of thin films using resonance ultrasound spectroscopy and determined the elastic constants of chemical-vapor-deposition diamond thin films. Mechanical resonance frequencies of a film/substrate layer specimen were measured, from which elastic constants of the thin film were determined by an inverse calculation. Mode identification for observed resonance frequencies is the key for their successful determination. We achieved this by measuring the displacement distribution on the vibrating-specimen surface. Determined elastic constants are smaller than those of bulk diamond, and they are elastically anisotropic between in-plane and out-of-plane directions. We attribute these compliant and anisotropic thin films to the incohesive bond at grain boundaries. A micromechanics model consistently explains the observation.

Viscosity and elastic constants of thin films of amorphous Te alloys used for optical data storage

The biaxial modulus and the linear coefficient of thermal expansion of sputtered amorphous Ge4Sb1Te5, Ge2Sb2Te5, and Ag0.055In0.065Sb0.59Te0.29 thin films were determined from stress versus temperature measurements on two different substrates. Viscous flow was measured by stress relaxation at constant temperature using wafer curvature measurements. The shear viscosity increased linearly with time, which can be attributed to bimolecular structural relaxation kinetics. The isoconfigurational activation energy was 1.94±0.09 eV for Ge4Sb1Te5, 1.76±0.05 eV for Ge2Sb2Te5, and 1.33±0.09 eV for AgInSbTe. These values scale with the absolute melting temperatures of the material.

Local elastic constants in thin films of an fcc crystal.

In this work we present a formalism for the calculation of the local elastic constants in inhomogeneous systems based on a method of planes. Unlike previous work, this formalism does not require the partitioning of the system into a set of finite volumes over which average elastic constants are calculated. Results for the calculation of the local elastic constants of a nearest-neighbor Lennard-Jones fcc crystal in the bulk and in a thin film are presented. The local constants are calculated at exact planes of the (001) face of the crystal. The average elastic constants of the bulk system are also computed and are consistent with the local constants. Additionally we present the local stress profiles in the thin film when a small uniaxial strain is applied. The resulting stress profile compares favorably with the stress profile predicted via the local elastic constants. The surface melting of a model for argon for which experimental and simulation data are available is also studied within the framework of this formalism.

Measurements of elastic constants in thin films of colossal magnetoresistance material.

Measurements of elastic constants of strained 200 and 400 nm thin films, as well as unstrained samples, of the colossal magnetoresistance (CMR) material La0.67Ca0.33MnO3 are presented. Since the peak resistance temperature of a strained CMR film decreases as the film thickness decreases, it is of interest to see if features in the elastic constants, reflecting structural or magnetic changes, follow the peak resistance temperature. It is observed that features in the elastic constants appear not only at the peak resistance temperatures of the CMR samples, but also at a temperature about 17 K higher. A new technique, thin-film resonant ultrasound spectroscopy, was used to make the measurements.

OS06W0137 Acoustic spectroscopy for measuring anisotropic elastic constants of thin films

This paper presents an advanced technique to determine all independent elastic constants C_<ij> of thin films. Many polycrystalline films exhibit elastic anisotropy between the film-growth direction and in-plane direction, and macroscopically possess five independent elastic constants; they are denoted by C_<11>, C_<33>, C_<13>, C_<44>, and C_<66> when the x_3 axis is chosen along the film-growth direction. All of C_<ij> of thin film affect the mechanical resonance frequencies of a film/substrate specimen. Measuring them permits us to determine the film C_<ij> with known density, dimensions, and the elastic constants of the substrate. It is necessary to measure the resonance frequencies with a high accuracy, because the contributions of the film C_<ij> to the resonance frequencies are normally small. We made this possible using the piezoelectric tripod, which consists of two piezoelectric pinducers and a supporting pin. The specimen is held on the tripod and only the specimen weight makes the acoustic coupling. This weak but stable coupling measures the resonance frequencies with a high accuracy. We applied our technique to copper thin films and found anisotropy between C_<11> and C_<33>.

Axisymmetric indentation of an incompressible elastic thin film

Indentation has been used to measure material properties in small volumes. This work presents a rigorous analysis of an incompressible elastic thin film indented by a rigid spherical or conical indenter under conditions that the contact radius is much larger than the film thickness and the contact condition between the indenter and the film is frictionless. Closed-form solutions for the load–displacement relationship and the contact stiffness are derived in terms of the ratio of the contact radius to the film thickness and material properties. It turns out that they are different from those obtained for the indentation of an elastic half-space. The contact stiffness is proportional to the contact area and inversely proportional to the film thickness for the frictionless boundary condition between the film and the substrate. For perfect bonding between the film and the substrate, the contact stiffness is proportional to the square of the contact area and inversely proportional to the cube of the film thickness. The results provide a guideline for measuring the elastic constants of thin films and determining the degree of adhesion between a thin film and a stiffer substrate.