Buckling Of Thin Film Research Articles

Elastic Properties of Supported Polycrystalline Thin Films and Multilayers: an X-Ray Diffraction Study

Numerous experimental and theoretical studies have shown that thin film elastic behavior may be different from the bulk one due to size effects related to grain boundaries, free surfaces and interfaces. In addition, thin films often present high compressive residual stresses which may be responsible of thin film buckling. These two features will be discussed in this communication through recent x-ray diffraction experiments: in situ tensile testing for elastic constant analysis and scanning x-ray micro diffraction for stress relaxation measurements associated with film buckling.

Fracture patterns in thin films and multilayers

ABSTRACTWhile there are many stress relief mechanisms observed in thin films, excessive residual and externally applied stresses cause film fracture. In the case of tensile stress a network of through-thickness cracks forms in the film. In the case of compressive stress thin film buckling is observed in the form of blisters. Thin film delamination is an inseparable phenomenon of buckling. The buckling delamination blisters can be either circular, straight, or form periodic buckling patterns commonly known as telephone cord delamination morphology.While excessive biaxial residual stress is the key for causing thin film fracture, either in tension, or compression, it is the influence of the external stress that can control the final fracture pattern. In this paper we consider phone cord buckling delamination observed in compressed W/Si and TiWN/GaAs thin film systems, as well as spiral and sinusoidal though-thickness cracks observed in Mo/Si multilayers under 3-point high-temperature bending in tension.

Evolution of normal stress and surface roughness in buckled thin films

In this work we investigate buckling of compressed elastic thin films, which are bonded onto a viscous layer of finite thickness. It is found that the normal stress exerted by the viscous layer on the elastic film evolves with time showing a minimum at early buckling stages, while it increases at later stages. The normal stress also shows a minimum as a function of applied compressive stress, which depends strongly on the viscosity of the underlying layer and strain values. Furthermore, with decreasing viscosity the film roughness amplitude also shows a minimum at early buckling stages. The effect of the viscosity becomes more pronounced with increasing strain in the film. Finally, decreasing elastic film thickness and/or increasing viscous layer thickness also enhance buckling roughness.

Macro Stress Mapping on Thin Film Buckling

Thin films deposited by Physical Vapour Deposition techniques on substrates generally exhibit large residual stresses which may be responsible of thin film buckling in the case of compressive stresses. Since the 80's, a lot of theoretical work has been done to develop mechanical models but only a few experimental work has been done on this subject to support these theoretical approaches and nothing concerning local stress measurement mainly because of the small dimension of the buckling (few 10th mm). This paper deals with the application of micro beam X-ray diffraction available on synchrotron radiation sources for stress mapping analysis of gold thin film buckling.

Residual stress mapping by micro X-ray diffraction: Application to the study of thin film buckling

Thin films deposited by Physical Vapour Deposition techniques on substrates generally exhibit large residual stresses which may be responsible of spontaneous detachment of the film from its substrate and in the case of compressive stresses, thin film buckling. Although these effects are undesirable for future applications, one may take benefit of it for thin film mechanical properties investigation. Since the 80's, a lot of theoretical works have been done to develop mechanical models with the aim to get a better understanding of driven mechanisms giving rise to this phenomenon and thus to propose solutions to avoid such problems. Nevertheless, only a few experimental works have been done on this subject to support these theoretical results and nothing concerning local stress/strain measurement mainly because of the small dimension of the buckling (few tenth mm). This paper deals with the application of micro beam x-ray diffraction available on synchrotron radiation sources for stress/ strain mapping analysis of gold thin film buckling.

The characterization of telephone cord buckling of compressed thin films on substrates

The topology of the telephone cord buckling of compressed diamond-like carbon films (DLC) on glass substrates has been characterized with atomic force microscopy (AFM) and with the focused ion beam (FIB) imaging system. The profiles of the several buckles have been measured by AFM to establish the symmetry of each repeat unit, revealing similarity with a circular buckle pinned at its center. By making parallel cuts through the buckle in small, defined locations, straight-sided buckles have been created on the identical films, enabling the residual stress in the film to be determined from the profile. It has been shown that the telephone cord topology can be effectively modeled as a series of pinned circular buckles along its length, with an unpinned circular buckle at its front. The unit segment comprises a section of a full circular buckle, pinned to the substrate at its center. The model is validated by comparing radial profiles measured for the telephone cord with those calculated for the pinned buckle, upon using the residual stress in the film, determined as above. Once validated, the model has been used to determine the energy release rate and mode mixity, G( ψ). The results for G( ψ) indicate that the telephone cord configuration is preferred when the residual stress in the DLC is large, consistent with observations that straight-sided buckles are rarely observed, and, when they occur, are generally narrower than telephone cords. Telephone cords are observed in many systems, and can be regarded as the generic morphology. Nevertheless, they exist subject to a limited set of conditions, residing within the margin between complete adherence and complete delamination, provided that the interface has a mode II toughness low enough to ensure that the buckle crack does not kink into the substrate.

An experimental study of the influence of imperfections on the buckling of compressed thin films

The role of imperfections on the initiation and propagation of buckle driven delaminations in compressed thin films has been demonstrated using experiments performed with diamond-like carbon (DLC) films deposited onto glass substrates. The surface topologies and interface separations have been characterized by using the Atomic Force Microscope (AFM) and the Focused Ion Beam (FIB) imaging system. The wavelengths and amplitudes of numerous imperfections have been measured by AFM and the interface separations characterized on cross sections made with the FIB. Chemical analysis of several sites, performed using Auger Electron Spectroscopy (AES), has revealed the origin of the imperfections. The incidence of buckles has been correlated with the imperfection wavelength. The findings have been rationalized in terms of theoretical results for the effect of imperfections on the energy release rate.

Atomic force microscopy study of the morphological shape of thin film buckling

Thin films elaborated by sputtering methods often develop very high internal compressive stresses and are then susceptible to delamination and buckling. The various buckling patterns have been investigated by atomic force microscopy and are reviewed and discussed in the frame of elastic theory.

Experiments with in-situ thin film telephone cord buckling delamination propagation

ABSTRACTThere are many different stress relief mechanisms observed in thin films. One of the mechanisms involves film debonding from the substrate. In the case of tensile residual stress a network of through-thickness cracks forms in the film. In the case of compressive residual stress thin film buckling and debonding from the substrate in the form of blisters is observed. The buckling delamination blisters can be either straight, or form periodic buckling patterns commonly known as telephone cord delamination morphology.The mechanics of straight-sided blisters is well understood. Current study relies on the in-situ observation of phone cord delamination propagation in different thin film/substrate systems. Both straight and phone cord delaminations are shown to simultaneously propagate in the same film system. Straight-sided blisters propagate several times faster than the phone cords, and may be followed by thin film fracture along the line of maximum film buckling amplitude. Phone cord delaminations originally start as straight-sided blisters, but then deviate to the periodic phone cord geometry due to the fact that the compressive residual stress in the film is biaxial. Digital analysis of motion recordings shows that partial crack “healing” is present at the curved portions of the phone cords due to the “secondary” buckling pushing thin film back to the substrate. These experimental observations allow for the correct interpretation of the telephone cord delamination morphology.

Rigorous Bounds for the Föppl—von Kármán Theory of Isotropically Compressed Plates

We study the Foppl—von Karman theory for isotropically compressed thin plates in a geometrically linear setting, which is commonly used to model weak buckling of thin films. We consider generic smooth domains with clamped boundary conditions, and obtain rigorous upper and lower bounds on the minimum energy linear in the plate thickness σ . This energy is much lower than previous estimates based on certain dimensional reductions of the problem, which had lead to energies of order 1+σ (scalar approximation) or σ2/3 (two-component approximation).

Pattern formation during delamination and buckling of thin films

Using a simple lattice model, we study the failure of compressively strained thin films on solid substrates. Our simulations reproduce much of the observed phenomenology of thin film blistering. In particular, we observe a peculiar form of stress relief in which a wrinkle of delaminated film propagates along a sinusoidal path. At higher intrinsic strains, the sinusoidal wrinkles bifurcate, forming branches. Finally, we identify a high-strain regime in which the film delaminates by forming a buckling front with many irregular lobes.

Spontaneous formation of ordered structures in thin films of metals supported on an elastomeric polymer

Spontaneous generation of complex order in apparently simple systems is both arresting and potentially useful1,2,3,4,5,6,7,8,9,10,11. Here we describe the appearance of complex, ordered structures induced by the buckling of thin metal films owing to thermal contraction of an underlying substrate. We deposit the films from the vapour phase on a thermally expanded polymer (polydimethylsiloxane, PDMS). Subsequent cooling of the polymer creates compressive stress in the metal film that is relieved by buckling with a uniform wavelength of 20–50 micrometres. The waves can be controlled and orientated by relief structures in the surface of the polymer, which can set up intricate, ordered patterns over large areas. We can account qualitatively for the size and form of the patterned features in terms of the non-uniform stresses developed in the film near steps on the polymer substrate. This patterning process may find applications in optical devices such as diffraction gratings and optical sensors, and as the basis for methods of strain analysis in materials.

A finite element analysis of configurational stability and finite growth of buckling driven delamination

A theoretical study of a budding-driven, initially circular, delaminated thin film loaded in equal bi-axial compression is presented. The main objective of this investigation is to study the configurational instability phenomena frequently observed for thin debonded coatings loaded in compression. The analyses are done with the aid of a kinematically non-linear finite element formulation of the plate problem to model the film, supplemented with a method to account automatically for the redistribution of the stress field as the shape of the advancing delamination is changing. By this procedure, not only the shape of the delaminated film but also the stability properties of the growth follow automatically. The configurational stability properties of the initially circular delamination are assessed by slightly perturbing the delamination front. The configurational instability is strongly related to the fracture mode dependence in the crack growth law. Finite growth of the buckling-driven thin film was also investigated. A load perturbation was employed as well as a front perturbation. It was found that the two perturbation methods can result in quite different shapes of the advancing buckled thin film. A few examples of extensive growth are also presented, and in some cases it was observed that a part of the delamination front may start tunnelling in the interface.

Cracking Mechanisms of Fine Lines by Microwedge Scratch Testing

ABSTRACTThree types of cracks associated with interfacial failure of a tungsten fine line on silicon oxide (SiO2) have been observed in microwedge scratch testing (MWST) of fine lines. They were identified by carefully controlling scratch conditions in a continuous microindenter system1, in conjunction with SEM micrographs. The first type is a hinge crack, which is responsible for nucleating an interfacial crack. The driving force for the hinge crack is the difference in stress conditions in the middle on theline (plane strain) and the outside of the line (plane stress). The second type is the interfacial crack, which is driven by the movement of the microwedge. This crack is modelled by the finite element method (FEM) to obtain an interfacial work of adhesion value. The third type of crack is a spallation crack, and is driven by tensile strains associated with buckling of the thin film once the interfacial crack becomes sufficiently long. Tensile strains in the film at the maximum crack length are calculated by FEM in order to arrive at a value of thin film fracture strength. A brittle failure mechanism has beenconfirmed by a micrograph of a spalled piece exhibiting no perceptible plastic deformation.

Stability criteria for buckling of thin anodic films on aluminum

Striae are defects which are sometimes observed in anodic films. A special arrangement of the anodization cell was built in order to obtain a symmetric stress distribution resulting in a regular arrangement of striae along the outer perimeter of the oxide layer. This mechanical instability was analysed using Euler's method applied to thin cylindrical shells under compressive forces. By comparing the Euler critical stress value with the stress present owing to metal-metallic oxide volume expansion it is possible to obtain a measurement of the coating plastification energy or its ability to withstand or relieve the stresses which may arise during growth. The ratio between the aluminum oxide-aluminum work Δγ of adhesion per unit length and the bulk modulus E of the film-forming aluminum (hydrous) oxide was determined for coatings formed under various current densities; the ratio Δγ E was shown to increase with deposition current density. Adhesion is shown to be an effective factor in preventing the formation of coating striae.

The linearized buckling analysis of a composite beam with multiple delaminations

A simple model is described for predicting the linearized buckling load of a composite beam with multiple delaminations. The model employs an energy method and arbitrary assumed displacements. Lagrange multipliers are used to enforce the kinematic constraints and boundary conditions, enabling a variety of support conditions to be studied. The accuracy of the approach is verified by comparing results with previously published data and a series of finite element analyses. The effects of delamination depth and length on the buckling load are investigated in detail for beams with one and two delaminations. Euler or thin film buckling is observed in most cases. However, for a beam with two delaminations located so that there are two laminae of equal thickness, antisymmetric S-shaped buckling modes are observed for certain delamination lengths.

Non-round fibre production

A new 3D continuum model is developed to simultaneously describe cracks and dislocations in materials undergoing finite strain deformations. Significant advances are made to account for fracturing in a cubic symmetrical system and to correctly model the microscopic dislocation properties into a Time-Dependent Ginzburg–Landau formalism. In addition, the interaction between dislocations and free borders (crack lips, surfaces…) is naturally described. As an example, the model is used to investigate the effects of plasticity on the delamination and buckling of thin films deposited on substrates. It may also be helpful in any other situation where cracks and dislocations take place and in which finite strain effects must be considered.

Domain walls induced by a magnetic field applied normally to a buckled thin film

Domain walls induced by a magnetic field applied normally to a buckled thin film