Thin Film-substrate System Research Articles

Adhesion behavior of an extensible soft thin film-substrate system based on finite deformation theory

In this paper, we study the adhesion behavior of a circular and extensible plate adhered to a rigid substrate based on the finite deformation theory. The energy method is used to derive the governing equations associated with boundary conditions. Due to the highly nonlinear nature of the problem and undetermined parameters on the boundary conditions, we solve the system of equations by an optimization-based approach which has never been used to study the thin film-substrate system. We also perform a comparative study on the deformation of the plate based on the finite deformation theory, finite deformation theory assuming that the adhered part is inextensible and the infinitesimal theory. The results demonstrate that when the plate is very soft, the adhesion force is very large or the detachment between the substrate and plate is very large, the inextensibility of the adhered part of the circular plate will induce large error in predicting the mechanical response of the adhered slender structure.

Thermal conductivity of thin film-substrate systems from two-side scanning photothermal deflection measurements: Theoretical model and validation.

Photothermal deflection (PTD) has been frequently utilized to measure the thermal properties of thin solid films on a substrate. In the models commonly used to interpret PTD data, the substrate is assumed to be an ideal thermal insulator. This assumption poses important restrictions on the reliability of these thermal measurements and limits the possibility to use PTD for also measuring the specific heat of the samples. Simultaneous knowledge of specific heat and thermal diffusivity is necessary to determine the thermal conductivity of thin solid films. In this work, we calculated the phase and amplitude of the PTD signal at the two opposites sides (film-side and substrate-side) of a thin-film substrate system. We find that, on both sides, the phases of the PTD signal primarily depend on the thermal diffusivity of the thin film, while the amplitudes primarily depend on the specific heat. By using the phases and amplitudes at the two sides, we show that the accuracy of thermal conductivity measurements by PTD can be dramatically improved. We validate our theoretical model by measuring, in a scanning PTD apparatus, the thermal properties of gold thin films, which are in excellent agreement with, and improve on, existing data from the literature.

Nanoindentation data analysis of loading curve performed on DLC thin films: Effect of residual stress on the elasto-plastic properties

The present work is a contribution to the understanding of the mechanical behavior of DLC thin films through nanoindentation tests. DLC films of different thicknesses deposited by the PECVD process on a silicon substrate contain high residual compressive stresses when they are very thin and the stresses become relatively low and more relaxed as the film thickens. These different levels of residual stress influence the values of hardness (H) and Young's modulus (E) obtained when probing the film-substrate system by nanoindentation. It is observed that the DLC layers exhibit different mechanical behaviors even when they are deposited under the same conditions. It is proposed that the compressive stress induces structural modifications resulting in modifying the elasto-plastic properties of each thin film-substrate system. Data analysis of the loading curve can provide information on the elasto-plastic properties of DLC thin films, particularly the stiffness (S) and Er2/H, as a function of residual compressive stresses. The structural changes induced by residual stresses were probed by using Raman spectroscopy and correlated to the mechanical properties.

Real-time stress evolution in a high temperature superconducting thin film caused by a pulse magnetic field

The high temperature superconducting YBa2Cu3O7−x films are widely used in various classes of microwave devices and these structures often undergo pulse magnetic field in applications. The stress behavior is of relevance to understand the mechanical response and important for assessing the safety of these superconducting structures. In this paper, we construct a theoretic model to analyze the stress behavior of a superconducting thin film-substrate system under a pulse loading (magnetic field), which is different with the well-known theoretic framework based on the Stoney formula. In the case of radial symmetry, the relationship between the stress of thin film and the electromagnetic body force is derived analytically. When a pulse loading is exerted on this film-substrate system, an analytical expression of stress dependent on the film curvature is presented, which can be considered as the foundation for the further experimental measurement. Moreover, we extend the coherent gradient sensor to kinetic measurement of the full field curvature. Using the presented model and the experimental technique, the full field stress and its evolution with time of a superconducting thin film-substrate system under a pulse magnetic field are obtained.

Stress Fields Induced by Dislocation Loops in Isotropic CuNb Film- Substrate System

Based on linear superposition rules and fast discrete Fourier transformation, a semi-analytical solution is developed for calculating the elastic fields induced by dislocation loops in an isotropic thin film-substrate system. The elastic field problem of thin film-substrate system is decomposed into two sub-problems: bulk stress due to a dislocation loop in an infinite space, and correction stress induced by free surface and interface of the film-substrate system. Correction elastic field is linearly superimposed onto bulk elastic field to produce continuous displacement and traction stress across the interface plane of the perfectly-bounded film-substrate system. Firstly, calculation examples of dislocation loops in Cu-Nb film-substrate system are performed to demonstrate the calculation efficiency of the developed semi-analytical approach. Then, elastic fields of dislocation loops within Cu film and Nb substrate of the Cu-Nb film-substrate system are analyzed. Finally, effects of film thickness, loop positions are investigated, and it is found that the elastic fields of dislocation loop are influenced remarkably by these two factors.

Thin film interface stresses produced by high amplitude laser generated surface acoustic waves

Surface acoustic waves (SAWs) have been explored for nondestructive metrology of thin film elastic properties and thickness due to confinement of their energy within a shallow depth from a material surface. In this paper, we study the dynamic interfacial stresses produced by high amplitude SAWs generated by a strongly ablative source in a thin film-substrate system, with the goal of investigating the possibility of inducing thin film delamination at high loading rates. For modeling purposes, we represent the mechanical loading resulting from the pulsed laser-sample interaction in the ablative regime by an equivalent compressive surface load, and the resulting stresses and particle velocities induced by the generated SAWs are calculated using a linear finite element model. We explore the numerical model to study the dependence of the film-substrate interface tractions on the ratio of the film thickness and SAW wavelength for a soft film on a stiff substrate. Furthermore, by matching the numerical results obtained from the finite element model with experimental results, we are able to predict the dynamic interfacial stresses for a copper film on a fused silica substrate produced by SAWs excited by a high power pulsed laser line source. This study has implications for exploring SAWs in the characterization of interfacial failure in thin-film substrate systems.

Tribological characterization of chemical vapor deposited Co and Co3O4 thin films for sensing reliability in engineering applications

In the present study, nanoindentation and nanoscratch techniques are applied in order to obtain the nanomechanical properties (hardness, H, and elastic modulus, E) of chemical vapor deposited Co and Co3O4 thin films (promising candidates for magnetic sensing and data storage applications) and evaluate the functionality of the thin film–substrate system. A wear analysis is also performed based on the H/E ratio.

Correlation between properties of HfO2 films and preparing parameters by ion beam sputtering deposition

Ion beam sputtering is one of the most important technologies for preparing hafnium dioxide thin films. In this paper, the correlation between properties of hafnium dioxide thin films and preparing parameters was systematically researched by using the orthogonal experiment design method. The properties of hafnium oxide films (refractive index, extinction coefficient, deposition rate, stress, and inhomogeneity of refractive index) were studied. The refractive index, extinction coefficient, physical thickness, and inhomogeneity of refractive index were obtained by the multiple wavelength curve-fitting method from the reflectance and transmittance of single layers. The stress of thin film was measured by elastic deformation of the thin film-substrate system. An orthogonal experimental strategy was designed using substrate temperature, ion beam voltage, ion beam current, and oxygen flow rate as the variables. The experimental results indicated that the temperature of the substrate is the key influencing parameter on the properties of hafnium oxide films, while other preparing parameters are also correlated with specific properties. The experimental results are significant for selecting proper parameters for preparing hafnium oxide films with different applications.

Asymptotic solutions for buckling delamination induced crack propagation in the thin film-compliant substrate system

In a thin film-substrate system in-plane compressive stress is commonly generated in the film due to thermal mismatch in operation or fabrication process. If the stress exceeds a critical value, part of the film may buckle out of plane along the defective interface. After buckling delamination, the interface crack at the ends may propagate. In the whole process, the compliance of the substrate compared with the film plays an important role. In this work, we study a circular film subject to compressive stress on an infinitely thick substrate. We study the effects of compliance of the substrate by modeling the system as a plate on an elastic foundation. The critical buckling condition is formulated. The asymptotic solutions of post-buckling deformation and the corresponding energy release rate of the interface crack are obtained with perturbation methods. The results show that the more compliant the substrate is, the easier for the film to buckle and easier for the interface crack to propagate after buckling.

Photoacoustic elastic bending in thin film—Substrate system

Theoretical model for optically excited two-layer elastic plate, which includes plasmaelastic, thermoelastic, and thermodiffusion mechanisms, is given in order to study the dependence of the photoacoustic (PA) elastic bending signal on the optical, thermal, and elastic properties of thin film—substrate system. Thin film-semiconductor sample (in our case Silicon) is modeled by simultaneous analysis of the plasma, thermal, and elastic wave equations. Multireflection effects in thin film are included in theoretical model and analyzed. Relations for the amplitude and phase of electronic and thermal elastic bending in the optically excited two-layer mechanically-supported circular plate are derived. Theoretical analysis of the thermodiffusion, plasmaelastic, and thermoelastic effects in a sample-gas-microphone photoacoustic detection configuration is given. Two normalization procedures of the photoacoustic elastic bending signal in function of the modulation frequency of the optical excitation are established. Given theoretical model can be used for various photoacoustic detection configurations, for example, in the study of optical, thermal, and elastic properties of the dielectric-semiconductor or metal-semiconductor structure, etc., Theoretical analysis shows that it is possible to develop new noncontact and nondestructive experimental method—PA elastic bending method for thin film study, with possibility to obtain the optical, thermal, and elastic parameters of the film thinner than 1 μm.

基底和膜层-基底系统的赝布儒斯特角计算

基底和膜层-基底系统的赝布儒斯特角计算

The surface effect on the strain energy release rate of buckling delamination in thin film–substrate systems

Gurtin–Murdoch continuum surface elasticity model is employed to study the buckling delamination of ultra thin film–substrate system. The effects of surface deformation and residual stress on the large deflection of ultra thin film are considered in analysis. A concept of effective bending rigidity (EBR) for ultra thin plate is proposed on the basis of Gurtin–Murdoch continuum theory and the principle of minimum potential energy. The governing equations with EBR are formally consistent with the classical plate theory, including both small deflection and large deflection. A surface effect factor is introduced to decide whether there is need to consider the surface effect or not. Combining the buckling theory and interface fracture mechanics, we obtain analytical solutions of the critical buckling load and the energy release rate of the interface crack in the film–substrate system. It is seen that the surface deformation and residual stress have significant effects on the buckling delamination of ultra thin film–substrate system.

OS5-1-2 Characterization of Small-volume Materials with Nanocontact Images

Conventional nanoindentation testing generally uses a peak penetration depth of less than 10 % of thin-film thickness in order to measure film-only mechanical properties, without considering the critical thickness for a given thin film-substrate system. The uncertainties in this testing condition make the measurement of film mechanical property more difficult. Thus, we estimated the critical relative thickness of Au thin film by adopting the mechanism-based strain gradient plasticity theory. Au film's critical relative thickness was determined by 0.17 and subsequent strength evaluations were carried out for nanoindentations shallower than 204 nm. The yield strength of thin film was estimated by considering the force equilibrium around an indentation-induced plastic zone; the plastic zone dimension is a key information for this analysis. However, conventional approach has analogized the plastic zone radius from few cross-sectional line profiles of the remnant indent and yielded erroneous strength result. Thus, we tried to extract a two-dimensional closed boundary of the plastic zone in this study by plotting a contour graph for the surface pile-up. This image processing was applied to the strength characterization of 1.2 μm-thick Au film on Si substrate. However, the analyzed indentation data produced strength overestimations compared to the microtensile results. This discrepancy in the yield strength was discussed from a viewpoint of microstructural anisotropy in the Au thin film.

Stress field due to a dislocation loop in a heterogeneous thin film–substrate system

In this paper, a superposition method is proposed to compute the stress field due to a dislocation loop in a heterogeneous thin film–substrate system. The problem is decomposed into two sub-problems: the stresses due to a dislocation loop in an infinitely extended bi-material space and the stresses induced by equivalent tractions on the free surface. The area-integral expression of the former is further reformulated in a line-integral form. Taking advantage of the Galerkin potential method and the Fourier transform, this paper then derives the elastic field in a heterogeneous thin film–substrate system due to surface loading. Numerical results demonstrate that both the free surface and the material heterogeneity have great influence on the stress field due to a dislocation loop.

Post-Yielding Stress-Strain Determination Using Spherical Indentation

In this research, finite element (FE) simulations were performed to verify Tabor's empirical relations that enable the use of the indentation test for determination of post-yielding uniaxial stress-strain curves of a variety of ductile metallic alloys. Both piling-up and sinking-in materials are included in this study. From the FE spherical indentation simulations, the indentation loads and projected contact radii are obtained for various elastic power-law plastic solids in both bulk and thin film substrate systems. It is found that for bulk materials, the indentation stresses and strains obtained from Tabor's empirical formula agreed well with the input uniaxial stress-strain data. This approach is then verified experimentally by spherical indentation tests on Inconel 783 alloy. In thin film substrate system, two cases, soft film on hard substrate and hard film on soft substrate were studied and the substrate effect on Tabor's relation was analyzed.

On the Characterization of Thin Film-only Mechanical Property Based on the Indentation Image Analysis

AbstractConventional nanoindentation testing generally uses a peak penetration depth of less than 10 % of thin-film thickness in order to measure film-only mechanical properties, without considering the critical depth for a given thin film-substrate system. The uncertainties in this testing condition make hardness measurement more difficult. We propose a new way to determine the critical relative depth for general thin-film/substrate systems; an impression volume analyzed from the remnant indent image is used here as a new parameter. Nanoindents made on soft Cu and Au thin films with various indentation loads were observed by atomic force microscope. The impression volume calculated from 3D remnant image was normalized by the indenter penetration volume. This indent volume ratio varied only slightly in the shallow regime but decreased significantly when the indenter penetration depth exceeded the targeted critical relative depth. Thus, we determined the critical relative depth by empirically fitting the trend of the indent volume ratio and determining the inflection point. The critical relative depths for Cu and Au films were determined as 0.170 and 0.173, respectively, values smaller than 0.249 and 0.183 determined from the hardness variation of the two thin films. Hence the proposed indent volume ratio is highly sensitive to the substrate constraint, and stricter control of the penetration depth is needed to measure film-only mechanical properties.

Propagation of Surface Acoustic Pulses Generated by a Femtosecond Laser in Thin Films on Solid Substrates

The technique of phase velocity dispersion measurements of surface acoustic waves in a thin film-substrate system was demonstrated. The excitation of surface acoustic waves (SAWs) was quite efficient with femtosecond laser pulses, and the damage of the surface was minimized. The measurements were performed with films of Al deposited on silicon wafers. The errors in the determination of the phase velocity and absorption were analyzed. The temperature changes in the propagation velocity on bare Si wafers were also measured. The data obtained permitted estimation of the accuracy of the temperature determination from measurements with SAW pulses.

A shaft-loaded blister test for elastic response and delamination behavior of thin film–substrate system

The elastic response of a thin film of photoresist deposited on a silicon wafer is studied by using a shaft-loaded blister test method developed recently. Experiment data are compared with an analytical solution. Results demonstrated that under shaft loading, the thin film underwent a pure bending mode at small deformation and gradually transformed to a pure stretching mode at larger deformation. The effect of residual stress on elastic response is also studied. The delamination of thin film from substrate can be successfully measured under displacement control mode by the shaft-loaded blister test.

Dynamical thermal model for thin metallic film–substrate system with resistive heating

In this paper the dynamical thermal behavior of the thin metallic film–substrate system is theoretically and experimentally discussed. The thin film–substrate system is considered as a bimaterial and the heat source used is the Joule effect on the metallic film when an electrical current is applied through the film. In order to obtain a physical picture of the temporal distribution of temperature on the film and substrate, a dynamic thermal model is proposed. This model has the feasibility to predict the temperature profile on the film and substrate, and to describe the dependence of geometrical, environmental, and material parameters of the system, on its thermal response. Experimental measurements on gold/glass and Al/Si(100) systems were performed and compared with the proposed model. The bimaterial thermal model proposed reproduces our experimental results with high accuracy. The model can be readily extended to study any kind of bimaterial system. The model is also appropriate to study multilayer thin film solar cells and to estimate thermal conditions on microelectromechanic (MEM) devices.

Evaluation of Film-Substrate Interface Durability Using a Shaft-Loaded Blister Test

In this paper, an analytical solution is presented for a shaft-loaded blister test for a thin film-substrate system. Both bending and stretching modes of deformation of the film are considered in the model. It is suggested that film-substrate delamination behavior under a Mode I separation load is governed by a parameter that relates the membrane stress to the rigidity of the film. The delamination behavior of several model thin film-substrate systems under repeated mechanical loads is studied. It is suggested from the results that film-substrate delamination under cyclic load depends on film rigidity, loading frequency, and film-substrate interfacial characteristics.