1. Introduction and overview 2. Film stress and substrate curvature 3. Stress in anisotropic and patterned films 4. Delamination and fracture 5. Film buckling, bulging and peeling 6. Dislocation formation in epitaxial systems 7. Dislocation interactions and strain relaxation 8. Equilibrium and stability of surfaces 9. The role of stress in mass transport.

Thin Film Materials: Stress, Defect Formation and Surface Evolution

Recent development in 2D materials beyond graphene

A two-dimensional (2D) porous layer can make an ideal membrane for separation of chemical mixtures because its infinitesimal thickness promises ultimate permeation. Graphene—with great mechanical strength, chemical stability, and inherent impermeability—offers a unique 2D system with which to realize this membrane and study the mass transport, if perforated precisely. We report highly efficient mass transfer across physically perforated double-layer graphene, having up to a few million pores with narrowly distributed diameters between less than 10 nanometers and 1 micrometer. The measured transport rates are in agreement with predictions of 2D transport theories. Attributed to its atomic thicknesses, these porous graphene membranes show permeances of gas, liquid, and water vapor far in excess of those shown by finite-thickness membranes, highlighting the ultimate permeation these 2D membranes can provide.

https://science.sciencemag.org/content/sci/344/6181/289.full.pdf

Ultimate permeation across atomically thin porous graphene.

Atoms at a free surface experience a different local environment than do atoms in the bulk of a material. As a result, the energy associated with these atoms will, in general, be different from that of the atoms in the bulk. The excess energy associated with surface atoms is called surface free energy. In traditional continuum mechanics, such surface free energy is typically neglected because it is associated with only a few layers of atoms near the surface and the ratio of the volume occupied by the surface atoms and the total volume of material of interest is extremely small. However, for nano-size particles, wires and films, the surface to volume ratio becomes significant, and so does the effect of surface free energy. In this paper, a framework is developed to incorporate the surface free energy into the continuum theory of mechanics. Based on this approach, it is demonstrated that the overall elastic behavior of structural elements (such as particles, wires, films) is size-dependent. Although such size-dependency is negligible for conventional structural elements, it becomes significant when at least one of the dimensions of the element shrinks to nanometers. Numerical examples are given in the paper to illustrate quantitatively the effects of surface free energy on the elastic properties of nano-size particles, wires and films.

Surface free energy and its effect on the elastic behavior of nano-sized particles, wires and films

A new analysis of the deflection of square and rectangular membranes of varying aspect ratio under the influence of a uniform pressure is presented. The influence of residual stresses on the deflection of membranes is examined. Expressions have been developed that allow one to measure residual stresses and Young's moduli. By testing both square and rectangular membranes of the same film, it is possible to determine Poisson's ratio of the film. Using standard micromachining techniques, free-standing films of LPCVD silicon nitride were fabricated and tested as a model system. The deflection of the silicon nitride films as a function of film aspect ratio is very well predicted by the new analysis. Young's modulus of the silicon nitride films is 222 ± 3 GPa and Poisson's ratio is 0.28 ± 0.05. The residual stress varies between 120 and 150 MPa. Young's modulus and hardness of the films were also measured by means of nanoindentation, yielding values of 216 ± 10 GPa and 21.0 ± 0.9 GPa, respectively.

/pdf/a-new-bulge-test-technique-for-the-determination-of-young-s-k7jzhg0p29.pdf

A new bulge test technique for the determination of Young's modulus and Poisson's ratio of thin films

Since its first application to thin films in the 1950's the bulge test has become a standard technique for measuring thin film mechanical properties. While the apparatus required for the test is simple, interpretation of the data is not. Failure to recognize this fact has led to inconsistencies in the reported values of properties obtained using the bulge test. For this reason we have used the finite element method to model the deformation behavior of a thin film in a bulge test for a variety of initial conditions and material properties. In this paper we will review several of the existing models for describing the deformation behavior of a circular thin film in a bulge test, and then analyze these models in light of the finite element results. The product of this work is a set of equations and procedures for analyzing bulge test data that will improve the accuracy and reliability of this technique.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0884291400017027

Analysis of the accuracy of the bulge test in determining the mechanical properties of thin films

Analysis and sample preparation techniques for the bulge test have been improved to the point where the test can provide reliable and accurate measurements of the mechanical properties of thin films. Ag-Pd multilayer films of variable bilayer period were prepared for this study and characterized by cross-section transmission electron microscopy and by x-ray methods. The films were tested in the bulge test to determine their biaxial moduli. The data show no peak in biaxial modulus at a critical composition wavelength and no nonlinear elastic behavior. They do show a slight trend toward increasing elastic modulus with increasing strength of (111) crystallographic texture. These findings refute a previous report of the “supermodulus” effect in this system and add to the evidence that the effect is caused by artifacts of the mechanical testing technique. Methods for eliminating such artifacts are discussed.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0884291400072617

The elastic biaxial modulus of ag-pd multilayered thin films measured using the bulge test

In this paper we address possible causes for inconsistencies in bulge test results and describe methods by which the bulge test technique can be made to produce accurate and reliable results. Experiments have been conducted on a variety of materials: polyimide (PIQ13) and polycarbonate (Lexan), silver and silver-palladium multilayers, and silicon nitride. All the materials tested yield biaxial moduli that are in the range of expected values for the bulk material. In addition, the tests show that the technique can be used to differentiate between the elastic properties of materials throughout the range of elastic stiffnesses, with even crystallo-graphic texture having a notable impact on the measured modulus. These results will be presented along with the methods used for preparing bulge test samples.

Accuracy and Reliability of Bulge Test Experiments

Since its first application to thin films in the 1950's, the bulge test has had a prominent place in the field of thin film mechanical properties. The major appeal of the technique is that it is analogous to the familiar uniaxial tension test, which is commonly applied to bulk materials. At the same time, it avoids the sample tearing and alignment problems associated with micro-tensile tests. Unfortunately, bulge test results have been sometimes controversial and difficult to reproduce. In this paper we address possible causes for mese inconsistencies and describe a method by which the bulge test technique can be made to produce accurate and reliable results.

Re-Examining the Bulge Test: Methods for Improving Accuracy and Reliability

The supermodulus effect has been reported as an anomalous increase of as much as several hundred percent in the elastic properties of certain compositionally-modulated thin metal films as the wavelength of the composition modulation decreases near 2 nm. Although elastic property variations have been detected by a variety of methods, including mechanical deflection experiments and acoustic measurements, the sign, magnitude and physical basis for such an effect remain in dispute. We report on the mechanical properties of compositionally-modulated Au-Ni and Ag-Pd thin films as determined by three different mechanical deflection experiments: nanoindentation, microbeam deflection and bulge testing. Au-Ni films were fabricated by alternately sputtering Au and Ni onto oxidized Si substrates and were tested by nanoindentation and microbeam deflection techniques. The nanoindentation experiments reveal a decrease of about 15% in the indentation modulus at a composition wavelength near 1.6 nm. The microbeam deflection experiments showed only small variations in in-plane stiffness but did reveal strongly wavelength-dependent substrate interaction stresses in these films. A simple analysis of the bulge test indicates that these stresses can reproduce the major features of the supermodulus effect, as reported from bulge test results, as artifacts of the analysis method. A more thorough evaluation of the bulge test shows that this technique can be used to obtain accurate and reproducible results if the initial and boundary conditions are properly accounted for. Ag-Pd films were also prepared by sputtering and were tested using improved sample preparation, bulge testing and data analysis techniques. Variations in the biaxial modulus were small and in agreement with the beam deflection results.

Martha K. Small

Papers

Analysis of the accuracy of the bulge test in determining the mechanical properties of thin films

The elastic biaxial modulus of ag-pd multilayered thin films measured using the bulge test

Accuracy and Reliability of Bulge Test Experiments

Re-Examining the Bulge Test: Methods for Improving Accuracy and Reliability

The Search for the Supermodulus Effect