The mechanical properties of thin films on substrates are described and studied. It is shown that very large stresses may be present in the thin films that comprise integrated circuits and magnetic disks and that these stresses can cause deformation and fracture to occur. It is argued that the approaches that have proven useful in the study of bulk structural materials can be used to understand the mechanical behavior of thin film materials. Understanding the mechanical properties of thin films on substrates requires an understanding of the stresses in thin film structures as well as a knowledge of the mechanisms by which thin films deform. The fundamentals of these processes are reviewed. For a crystalline film on a nondeformable substrate, a key problem involves the movement of dislocations in the film. An analysis of this problem provides insight into both the formation of misfit dislocations in epitaxial thin films and the high strengths of thin metal films on substrates. It is demonstrated that the kinetics of dislocation motion at high temperatures are expecially important to the understanding of the formation of misfit dislocations in heteroepitaxial structures. The experimental study of mechanical properties of thin films requires the development and use of nontraditional mechanical testing techniques. Some of the techniques that have been developed recently are described. The measurement of substrate curvature by laser scanning is shown to be an effective way of measuring the biaxial stresses in thin films and studying the biaxial deformation properties at elevated temperatures. Submicron indentation testing techniques, which make use of the Nanoindenter, are also reviewed. The mechanical properties that can be studied using this instrument are described, including hardness, elastic modulus, and time-dependent deformation properties. Finally, a new testing technique involving the deflection of microbeam samples of thin film materials made by integrated circuit manufacturing methods is described. It is shown that both elastic and plastic properties of thin film materials can be measured using this technique.

Mechanical properties of thin films

Dynamic crack growth is analysed numerically for a plane strain block with an initial central crack subject to tensile loading. The continuum is characterized by a material constitutive law that relates stress and strain, and by a relation between the tractions and displacement jumps across a specified set of cohesive surfaces. The material constitutive relation is that of an isotropic hyperelastic solid. The cohesive surface constitutive relation allows for the creation of new free surface and dimensional considerations introduce a characteristic length into the formulation. Full transient analyses are carried out. Crack branching emerges as a natural outcome of the initial-boundary value problem solution, without any ad hoc assumption regarding branching criteria. Coarse mesh calculations are used to explore various qualitative features such as the effect of impact velocity on crack branching, and the effect of an inhomogeneity in strength, as in crack growth along or up to an interface. The effect of cohesive surface orientation on crack path is also explored, and for a range of orientations zigzag crack growth precedes crack branching. Finer mesh calculations are carried out where crack growth is confined to the initial crack plane. The crack accelerates and then grows at a constant speed that, for high impact velocities, can exceed the Rayleigh wave speed. This is due to the finite strength of the cohesive surfaces. A fine mesh calculation is also carried out where the path of crack growth is not constrained. The crack speed reaches about 45% of the Rayleigh wave speed, then the crack speed begins to oscillate and crack branching at an angle of about 29° from the initial crack plane occurs. The numerical results are at least qualitatively in accord with a wide variety of experimental observations on fast crack growth in brittle solids.

Numerical simulations of fast crack growth in brittle solids

Computational modelling of impact damage in brittle materials

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

Size dependence of mechanical properties of gold at the micron scale in the absence of strain gradients

Preface List of symbols 1. Background and overview 2. Basic elastodynamic solutions for a stationary crack 3. Further results for a stationary crack 4. Asymptotic fields near a moving crack tip 5. Energy concepts in dynamic fracture 6. Elastic crack growth at constant speed 7. Elastic crack growth at nonuniform speed 8. Plasticity and rate effects during crack growth Bibliography Index.

Dynamic Fracture Mechanics

The Stability of a Dislocation Threading a Strained Layer on a Substrate

At high crack velocities in metallic materials nearly all plastic strain accumulates at very high strain-rates, typically in the range 10 3 s −1 to 10 5 s −1 . At these rates, dislocation motion is limited by dynamic lattice effects and the plastic strain-rate increases approximately linearly with stress. The problem for a crack growing at high velocity is posed for steady-state, small scale yielding in elastic/rate-dependent plastic solids. A general expression is derived for the near-tip stress intensity factor in terms of the remote intensity factor, or equivalently for the near-tip energy release-rate in terms of the overall release-rate. An approximate calculation of the plastic strain-rates provides this relation in analytical form. Imposition of the condition that the near-tip energy release-rate be maintained at a critical value provides a propagation equation for the growing crack. A single, nondimensional combination of material constants emerges as the controlling parameter. Implications for dynamic crack propagation are discussed.

High strain-rate crack growth in rate-dependent plastic solids

Fragmentation of brittle materials under high rates of loading is a commonly occurring phenomenon, but quantitative descriptions of the process have been elusive. Several models for dynamic fragmentation have been suggested in the past. In the present paper we consider two such models based on energy balance and compare their predictions of fragment size to the results of numerical simulations. This comparison shows that the energy-balance models lead to estimates of fragment size which are an order of magnitude larger than the calculated ones. These differences seem to be due to the fact that these energy-balance models deal with the onset of the fragmentation event; they do not include the time dependence of the process. In reality, fragmentation occurs over finite time during which energy continues to be supplied to the system, and cracks nucleate and propagate throughout the body. Therefore, we propose a model that includes the time history of the process and the number, distribution, and strength of flaws in the material. This model is studied by means of both simple analytical methods and computations. The results provide a consistent picture of fragmentation as a transient event.

Modeling and Simulation of Dynamic Fragmentation in Brittle Materials

The configuration of an elastically strained thin film bonded to a relatively thick elastic substrate over a plane interface is considered. The free energy of the system is taken to be the surface energy of the free surface, which is initially flat, and the elastic strain energy. It is assumed that the film material can change the shape of its free surface by means of mass diffusion along the surface, and that this mass transport occurs coherently. As a result of this diffusion process, the free energy of the system changes due to a change in surface shape and due to a change in the elastic energy. If the change in free energy as the surface shape departs from planar is positive, then this change will tend to occur spontaneously and the flat shape is unstable. The stability of a biaxially stressed thin film due to material diffusion over its surface is considered here under both two- and three-dimensional conditions. The stability condition is derived in the form of a difference between two positive definite quantities, one associated with surface energy and the other associated with strain energy, and the sign of this difference depends on the relative stiffnesses of the materials, the thickness of the film, the surface energy of the film material, and the initial elastic stress in the film. It is demonstrated that the configuration with a flat free surface is unstable under sinusoidal perturbations in the shape of the surface for any combination of parameters, provided that the wavelength of the perturbation is larger than some critical value. Numerical results are presented for the critical value as a function of film thickness for several values of the ratio of elastic stiffnesses of the materials.

L. B. Freund

Papers

Dynamic Fracture Mechanics

The Stability of a Dislocation Threading a Strained Layer on a Substrate

High strain-rate crack growth in rate-dependent plastic solids

Modeling and Simulation of Dynamic Fragmentation in Brittle Materials

Instability of a biaxially stressed thin film on a substrate due to material diffusion over its free surface