Elastic Constants Of Film Research Articles

Using Mechano-Electro-Chemical Coupling to Measure the Thin Film Elastic Constants, Thermo-Chemical Expansion Coefficients, and Oxygen Surface Exchange Coefficients of Praseodymium Doped Ceria Presentation Format: Oral Preferred

A Multi-beam Optical Stress Sensor (MOSS) is a curvature measurement platform which is commonly used to measure the film stress in bilayer samples. It has been widely used as an in-situ technique to measure the film stress during deposition.1 However, when combined with the dual substrate method proposed by Zhao et al,2 in situ curvature measurements can be used to measure Young’s moduli and thermo-chemical expansion coefficients simultaneously as a function of temperature. Using the curvature relaxation (κR) technique developed recently,3-5 oxygen surface exchange coefficients (kchem) can also be measured as a function of temperature using in situ curvature measurements. In this work, the Young’s moduli, thermo-chemical expansion coefficients and kchem values of praseodymium doped ceria (PCO) were measured as a function of temperature using a MOSS. First, phase pure Pr0.1Ce0.9O1.95 (PCO) powder was prepared through glycine nitrate combustion and subsequent calcination at 1100oC in air. This powder was then pressed in a stainless-steel die and fired to 1450oC to produce a pulsed laser deposition (PLD) target. In preparation for PLD, (001) oriented 9.5% yttria doped zirconia (YSZ) and (001) oriented magnesium oxide (MgO) substrates (Crystec, GmbH) were pre-annealed at 1450oC for 20 hours to remove residual stress within them. PCO PLD was then conducted at 680oC for 20 min, with a 10-2 torr oxygen partial pressure and 350 mJ power density. After deposition, the PCO bilayers were re-equilibrated with air by firing them in air at 1000oC for 1 hour. For dual substrates measurements, stress vs. temperature data for PCO|YSZ and PCO|MgO were collected with a 1oC/min heating rate and a 0.2oC/min cooling rate. The slopes of the stress vs. temperature curves can be expressed by: dσPCO|YSZ/dT = MPCO(αYSZ-αPCO) (1) dσPCO|MgO/dT = MPCO(αMgO-αPCO) (2) where is the stress of bilayer sample, T is the temperature, M is the biaxial modulus of the film, is the thermo-chemical expansion coefficient. With two unknowns and two equations, and were then extracted as a function of temperature. The Young’s moduli were then calculated from assuming a Poisson’s ratio of 0.33 as has been done previously for 6. For κR measurements, relaxation data were recorded at 650~725oC with 25oC increments. The oxygen partial pressure was switched between synthetic air (20%O2-80%Ar) and 10% diluted synthetic air (10% synthetic air-90%Ar). Figure 1 shows the Young’s modulus and thermo-chemical expansion coefficients measured here compared to other literature studies.6-8 In contrast to other studies the present study produced PCO Young’s moduli over a complete range of temperatures. In addition, the PCO Young’s moduli started to decrease significantly once the PCO started to become nonstoichiometric (as indicated by an uptick in chemical expansion in Figure 1b). The PCO kchem values (not shown) were in good agreement with the kchem values measured by other electrode-free techniques, such as optical relaxation.9 Figure 1

Characterization of silicon surface elastic constants based on different interatomic potentials

Mechanical properties of materials are an important factor in designing nanoscale systems. Several researches and experiments have shown that the mechanical properties of the nano-scale materials are different from those of bulk. One of the major reasons for this difference is that the ratio of surface to volume increases at the nano-scale, and the effects of free surfaces become very important. In this paper, we have measured the surface elastic constants of silicon crystalline structure using different interatomic potentials. The potentials employed here are EDIP (Environment-Dependent Interatomic Potential), Stillinger-Weber and Tersoff, and also different crystalline orientations are examined. In order to obtain surface elastic constants, we have first determined the lattice constant resulting in minimum energy of bulk model for each potential, then we have measured the bulk and film elastic constants using respective models. It is observed that by increasing film thickness, elastic constants approach to those of bulk. Next, using the results of the previous sections, the surface elastic constants are measured and discussed for different surfaces using different potentials.

Measurement of the Elastic Constants of a Columnar SiC Thin Film

The technique of resonant ultrasound spectroscopy was used to measure the elastic properties of a polycrystalline cubic silicon carbide (3C-SiC) thin film. The film, grown on a silicon (100) substrate, was 1.69 microns thick with columnar crystalline grains and a (111) texture. The substrate with the film was placed between two transducers and the resonant frequencies were measured; measurements were repeated after selective, timed dry etching of the film, allowing a determination of the elastic constants of the film alone. The film elastic constants, c(11)=371 and c(12)=146 GPa, were within a few percent of the literature values (c(11)=386, c(12)=136 GPa) of crystalline 3C-SiC. However, the film elastic constant c(44), 111 GPa, was significantly smaller than the bulk literature value, 254 GPa. For the film, c44 approximately (c(11)-c(12))/2, indicating that, quite unlike a bulk 3C-SiC crystal, the thin film is elastically isotropic.

Measurement of thin film elastic constants by X-ray diffraction

Uniaxial tensile testing on thin film/kapton composite specimens has been used to determine thin film elastic constants by X-ray diffraction. The method has been applied to a 140-nm-thick tungsten film which is elastically isotropic and to a 560-nm-thick gold film which is elastically anisotropic. The experimental ɛ-vs.-sin 2 ψ curves are linear for the polycrystalline isotropic tungsten film and nonlinear for the textured gold film. It is shown that a linear analysis of ɛ-vs.-sin 2 ψ curves allows the direct determination of elastic constants of the tungsten film, while the use of the crystallite-group method is proposed to analyse the nonlinear behaviour of ɛ-vs.-sin 2 ψ curves of the fibre-textured gold film.

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.

Size effect on intragranular elastic constants in thin tungsten films

The size effect on the elastic constants of nanocrystalline tungsten has been investigated in the case of W/Cu multilayers with two modulation wavelengths (3.1 and 24.0 nm). Tungsten Young’s modulus and Poisson’s ratio have been measured thanks to a technique coupling x-ray diffraction with in situ tensile testing. It is demonstrated that the in-grain thin film elastic constants are highly microstructure—sensitive: in the “3.1 nm” multilayer, tungsten Poisson’s ratio is larger than the bulk one while it is smaller in the “24.0 nm” multilayer; a softening of tungsten Young’s modulus is evidenced in the case of the specimen with the smallest period.

Instability and decomposition on the surface of strained alloy films

A continuum dynamical model is developed to determine the morphological and compositional instabilities on the free surface of heteroepitaxial alloy films in the absence of growth. We use linear stability analysis to study the early nonequilibrium processes of surface evolution, and calculate the stability conditions and diagrams for different cases of material parameters. There are two key considerations in our treatment: the coupling between top free surface of the film and the bulk phase underneath, and the dependence of both Young's and shear elastic moduli on local composition. The combination and interplay of different elastic effects caused by lattice misfit between film and substrate (misfit strain), composition dependence of film lattice parameter (compositional strain) and of film elastic constants lead to complicated and rich stability results, in particular the joint stability or instability for morphological and compositional profiles, the asymmetry between tensile and compressive layers, as well as the possible stabilization and suppression of surface decomposition even below the effective critical temperature. We also compare our results with the observations of some postdeposition annealing experiments.

Measurement of the elastic constants of nanometer-thick films

Reliable measurement of the elastic constants of films of nanometric thickness is needed for the development of several nanotechnologies, but is still an open issue, especially in the case of hard films. We show that by combining surface Brillouin scattering (SBS) and X-ray reflectivity (XRR) measurements, the elastic constants of nanometric supported films can be obtained. The dispersion relations of surface acoustic waves (SAWs) are measured by SBS. The same dispersion relations are computed as functions of substrate properties, and the film thickness, mass density and elastic constants. The film thickness and density are obtained by X-ray reflectivity measurements; the elastic constants are then derived by fitting the computed SAW dispersion relations to the measured ones. We present results obtained on tetrahedral amorphous carbon films, having thickness below 10 nm, deposited on silicon. We show that the elastic constants can be measured also for these ultrathin films.

Surface acoustic wave propagation properties of nitrogenated diamond-like carbon films

Nitrogenated diamond-like carbon (a-C:N) thin films on Si(100) were deposited by radio frequency magnetron reactive sputtering. Using ZnO piezoelectric thin films, the surface acoustic wave (SAW) propagation properties of a-C:N thin films on Si(100) have been experimentally investigated using bidirectional interdigital transducers between ZnO and a-C:N/Si(100). A generalized SAW mode with velocities between 5000 and 7000 m/s were observed. A high velocity pseudo-SAW mode was also observed and identified with simulated data, of which the velocity was 13 850 m/s. We calculated the film elastic constants from the phase velocities in the layered structure. The calculated constants for a-C:N thin films on Si were c11=392.1 and c44=185.7 GPa.

Elastic properties of GaSe films epitaxially grown on the Si(111)1 × 1-H surface, studied by Brillouin scattering

Brillouin light scattering has been used to study the elastic properties of GaSe films of different thicknesses epitaxially grown on a hydrogen-terminated non-reconstructed Si(111) surface. Both Rayleigh and Sezawa guided acoustic modes have been revealed, and their velocity dispersion measured as a function of the ratio between the film thickness and the acoustic wavelength. This enabled us to determine four of the five GaSe film elastic constants through a non-linear best fit procedure. The fifth elastic constant c66 was obtained from detection of shear horizontal waves in the thicker film. The results obtained show that the film constants are similar to those of the bulk material, except for the shear elastic constant c44 which is appreciably lower. The values of the elastic constants thus obtained were used to calculate the Brillouin cross-section taking into account the rippling induced by surface phonons both at the free surface and at the interface. This permitted us to achieve a satisfactory reproduction of the experimental spectra.

Brillouin scattering study of epitaxial InSe films grown on the surface

Brillouin light scattering has been used to study the elastic properties of an InSe film grown epitaxially on a hydrogen-terminated non-reconstructed Si(111) surface. Both generalized Rayleigh - Sezawa and Love acoustic modes have been revealed, and their velocity dispersions measured as functions of the ratio between the film thickness and the acoustic wavelength. This enabled us to determine the complete set of InSe film elastic constants through a non-linear best-fitting procedure.

Residual stress in stabilized zirconia thin films prepared by r.f. magnetron sputtering

Calcia-stabilized zirconia thin films were deposited by r.f. magnetron sputtering onto 2 inch 〈111〉 silicon substrates. Three samples of cubic phase, with thicknesses 0.36, 0.72 and 1.08 μm were deposited under the same operating conditions, and both thickness uniformity and surface roughness were controlled accurately by profilometry. The considerable residual stress field present in the samples was studied by two very different techniques: measurement of the substrate curvature by profilometry, and measurement of the thin film lattice strain by X-ray diffraction (XRD). The adopted XRD parallel beam geometry permitted also study of the texture developed; the main orientation was such that the angle between [111] directions of Si and CaO—ZrO2 was about 13°, with a fraction of crystallites grown along [111]Si∥[111]ZrO2. Residual stress values as high as 3 GPa were measured but, as is typical of many highly textured physically vapour deposited films, the sin2ψ method gave different stress values along different crystallographic directions and the trend of interplanar distances dhkl vs. sin2ψ was not always linear. The main reason for this behaviour is the anistropy of the thin film elastic constants, which has a strong effect particularly in highly textured materials. XRD data were evaluated following a recently proposed procedure which takes into account elastic anisotropy and thin film preferred orientations. The residual stress measured by XRD methods was systematically higher than that obtained from curvature measurements; this difference is discussed with reference to the hypotheses of the two methods and the nature of the stress in the film/substrate composite system.

The Determination of Elastic Constants Using a Combination of X-Ray Stress Techniques

AbstractThe powder diffraction x-ray technique commonly used to measure strain in polycrystalline materials requires a knowledge of the elastic constants in order to convert the strain into a stress value. For many materials, these constants are not always known. Another technique to measure strain is the x-ray lattice curvature (substrate bending) method which requires no knowledge of the film elastic constants. The strain is measured in the substrate and requires only the elastic constants of the substrate to convert the measured strain into stress. Using a combination of the powder diffraction technique and a double crystal lattice curvature technique, the elastic constants of TaSi2and WSi2have been determined for various crystallographic directions.

Brillouin Scattering from Surface Phonons in Thin Films

Brillouin scattering from thermal surface phonons has been observed in thin films deposited on semi-infinite media. The velocity of Rayleigh and Sezawa waves was measured and interpreted in terms of the film elastic constants. Surface phonon attenuations were also measured and it was found that the lifetimes of surface and bulk phonons of the same wave vector are comparable in the glass studied.

Thermal similarity in two and three dimensions: The Debye temperatures of bulk and adsorbed monolayerHe4

The Debye temperatures for two- and three-dimensional systems are compared using an isotropic elastic model that includes the effect of finite initial stress and assumes the Cauchy conditions. It is shown that the effect of initial pressure on sound speeds, Debye temperatures, and selected elastic properties is determined in both dimensions by the dimensionless product of pressure and compressibility. The model is applied to the observed similarity in Debye temperatures for monolayer and hcp bulk ${\mathrm{He}}^{4}$. Using 0 \ifmmode^\circ\else\textdegree\fi{}K compressibility and pressure data, there is essential agreement between the elastic model and the experimental bulk Debye temperatures. The agreement results from the effect of initial pressure, which softens the bulk Debye temperatures by as much as 20% relative to the zero-pressure values for the same compressibility. A large softening also occurs in the two-dimensional extension when applied to the ${\mathrm{He}}^{4}$-graphite adsorption system but, in contrast to the bulk, the two-dimensional spreading pressures are insufficient to produce comparable quantitative agreement with the experimental film Debye temperatures. The idealized model is extended to include a specific substrate effect by separating the total film elastic constants into two parts: An intrinsic (Cauchy) contribution associated with the two-dimensional adsorbate lattice and a secondary contribution identified with the substrate, which lifts the Cauchy conditions on the total elastic constants for the film. The required fractional substrate contribution to the bulk and shear moduli yielding agreement with the experimental film Debye temperatures is examined.