Buckling and cracking of thin films on compliant substrates under compression

It is shown that unless the substrate is at least as stiff as the film, the energy stored in the substrate contributes significantly to the energy release rate of film delamination under compression either with or without cracking. For very compliant substrates, such as polyethylene terephthalate (PET) with a indium tin oxide (ITO) film, the energy release rate allowing for the deformation of the substrate can be more than an order of magnitude greater than the value obtained neglecting the substrate's deformation. The argument that buckling delaminations tunnel at the tip rather than spread sideways because of increase in mode-mixity may need modification; it is still true for stiff substrates, but for compliant substrates the average energy release rate decreases with delamination width and the limitation in buckled width may be due to this stability as much as the increase in mode-mixity.     

The fracture of brittle thin films on compliant substrates in flexible displays

One mechanical issue in flexible organic light emitting displays (OLED) is the fracture of extremely thin brittle conducting transparent oxide films deposited on thin flexible substrates. Understanding the behaviour of these films under flexed condition is essential for designer of flexible OLED. Controlled buckling experiments on the film and substrate have been designed to study the fracture of the films under both tension and compression. Fracture of the film is superficially similar in both tension and compression. However, under tension a channelling crack is formed, while under compression, the film delaminates, buckles and cracks in a tunnelling motion. The fracture toughness of the film and the delamination toughness have been estimated from these experiments. Design to maximise the flexibility of the device is discussed.     

Channel-cracking of thin films with the extended finite element method

The recently developed extended finite element method (XFEM) is applied to compute the steady-state energy release rate of channeling cracks in thin films. The method is demonstrated to be able to model arbitrary singularities by using appropriate enriching functions at selected nodes with a relatively coarse mesh. The dimensionless driving force for channeling cracks is obtained as a function of elastic mismatch, crack spacing, and the thickness ratio between the substrate and the film. The results are compared with those from several previous studies when available. Emphasis is placed on the cases with compliant substrates, for which much less information is available from previous studies. It is found that, while it is quite challenging to model the cases with very compliant substrates using regular finite element method because of the strong singularities, the present approach using XFEM is relatively simple and straightforward.     

Extracting thin film hardness of extremely compliant films on stiff substrates

A previously reported method for extracting the thin film hardness from nanoindentation into a film on an elastically mismatched substrate was applied to four different cases of extreme mismatch in elastic properties: Parmax, Ultem, Polysulfone and Perfluorocyclobutyl polymer thin films on Si substrates. All of these cases represent extremely compliant films on a stiff substrate, where the ratio of film shear modulus to substrate shear modulus ranged from 0.008 to 0.036. Analyzing the nanoindentation data into these film/substrate systems poses a significant limitation when using the Oliver and Pharr method as the hardness increases rapidly with indentation depth. Therefore, a method involving the measured contact stiffnesses to more accurately determine the correct contact areas was used to extract the true hardness of the polymer thin films. The results indicate that our method is able to remove the substrate effects as well as the complications arising from pile-up and surface roughness to yield a wide plateau in hardness despite the extreme elastic mismatch conditions.     

A map of competing buckling-driven failure modes of substrate-supported thin brittle films

Our in situ experiments of polyimide-supported thin indium tin oxide (ITO) films reveal buckling-driven film cracking in some samples and buckling-driven interfacial delamination in other samples. Although studies of individual buckling-driven failure mode exist, it still remains unclear what governs the competition between these two different failure modes in a given film/substrate structure. Through theoretical analysis and numerical simulations, we delineate a map of competing buckling-driven failure modes of substrate-supported thin brittle films in the parameter space of interfacial adhesion and interfacial imperfection size. Such a map can offer insight on the mechanical durability of functional thin films. For example, interestingly, we show that strongly bonded thin brittle films are more prone to buckling-driven cracking, a more detrimental failure mode for thin brittle ITO transparent conductors widely used in displays and flexible electronics.     

Influence of interfacial delamination on channel cracking of elastic thin films

Channeling cracks in brittle thin films have been observed to be a key reliability issue for advanced interconnects and other integrated structures. Most theoretical studies to date have assumed no delamination at the interface, while experiments have observed channel cracks both with and without interfacial delamination. This paper analyzes the effect of interfacial delamination on the fracture condition of brittle thin films on elastic substrates. It is found that, depending on the elastic mismatch and interface toughness, a channel crack may grow with no delamination, with a stable delamination, or with unstable delamination. For a film on a relatively compliant substrate, a critical interface toughness is predicted, which separates stable and unstable delamination. For a film on a relatively stiff substrate, however, a channel crack grows with no delamination when the interface toughness is greater than a critical value, while stable delamination along with the channel crack is possible only in a small range of interface toughness for a specific elastic mismatch. An effective energy release rate for the steady-state growth of a channel crack is defined to account for the influence of interfacial delamination on both the fracture driving force and the resistance, which can be significantly higher than the energy release rate assuming no delamination.     

Nonlinear elastic mechanics of the ball-loaded blister test

The nonlinear elastic mechanics of spherically capped shaft or ball-loaded blister tests is presented. In the test model, a thin film is attached to a substrate with a circular hole running through the thickness of the substrate. A central load is applied to the film through the hole by a spherically capped shaft or a ball with a finite radius. The deformed blister is divided into two parts: a circular region in contact with the sphere of the cap or ball and an outer noncontact annulus. The Reissner’s plate theory is employed to describe the deformation of the contact part and the von Kármán plate theory for the noncontact annulus. A constitutive equation of coupled linear springs is obtained to quantify the effect of the substrate deformation on the blister deflection. For small deflection, the analytical solution of load-deflection is derived. For large deflection, an iteration approach is adopted to predict numerically the load-deflection curve. Finite-element analysis is conducted to verify the analytical and numerical solutions. The influence of the substrate deformation, residual stress, radius of the spherical cap or ball and the friction between the film and ball on the load-deflection relation is investigated.     

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.     

Channel cracking in thin films on substrates of finite thickness

Solutions are presented for the elastic plane-strain problem of a crack in a coating on a compliant substrate of finite thickness. Analysis of the problem shows that substrate thickness has a significant effect on the steady-state energy release rate for channel cracks. This is so over a wide range of elastic mismatch between film and substrate, but is especially important if the substrate is more compliant than the film. Relaxation of the film stress due to elastic deformation of the substrate also plays an important role. If the substrate is clamped around the edge, as would be the case for a coated membrane, the stress in the coating cannot relax and the energy release rate for channel cracking increases significantly with decreasing substrate thickness. If the film stress is allowed to relax, however, the driving force for cracking is reduced as the substrate thickness decreases. The results from this study are used to evaluate the change in curvature of a film/substrate assembly due to channel cracking, a quantity that is of interest for the experimental determination of stresses in thin films. An expression for the elastic extension of the substrate due to channel cracking is derived making it possible to evaluate the effect of cracking on the mechanical behavior of bilayer membranes. It is expected that the present study may lead to the development of new experimental techniques for measuring the fracture toughness of thin coatings.     

Fracture toughness measurement of thin films on compliant substrate using controlled buckling test

Thin films and multilayered structures are increasingly used in the industry. One of the important mechanical properties of these thin layers is the fracture toughness, which may be quite different from the known value of the bulk sample due to microstructural difference. In the design towards device flexibility and scratch resistance, for example, fracture toughness is an important parameter of consideration. This work presents a testing scheme using controlled buckling experiment to determine the fracture toughness of brittle thin films prepared on compliant substrates. When the film is under tension, steady-state channelling cracks form in parallel to each other. Critical fracture strain can be calculated by the measuring the displacement of the buckled plate. The fracture toughness can then be obtained with the help of finite element calculation. When the substrate experiences plastic deformation, the energy release rate is increased by the degree of plasticity. Fracture toughness measurement of two types of thin film Cu-Sn intermetallic compounds has been given to illustrate the merits of such a test scheme.     

Mechanical failure analysis of thin film transistor devices on steel and polyimide substrates for flexible display applications

The crack onset strain (COS) of 4-level thin film transistor (TFT) devices on both steel foils and thin polyimide (PI) films was investigated using tensile experiments carried out in situ in an optical microscope. Cracks initiated first within the SiO₂ insulator layer for both types of substrates. The COS was found to be equal to 1.15% and 0.24% for steel and PI, respectively. The influence of loading direction on failure of the TFT stack with anisotropic geometry was moreover found to be considerable, leading to recommendations for backplane design. The large difference in critical strain of the SiO₂ layer on the two substrates was analyzed using an energy release rate approach, and found to result from differences in layer/substrate mechanical contrast and in internal stress state. Based on this analysis a correlation between layer/substrate elastic contrast and tensile failure behavior was devised.     

Microstructural characterization of thin gold films on a polyimide substrate

The study of thin metal films on flexible substrates is of interest for manufacture of many devices, such as implantable electrode arrays consisting of gold film on polyimide substrates. Adhesion of the film to the substrate is of utmost importance for device durability. Gold adhesion to a polyimide has previously been shown to increase when a variety of substrate treatments are performed prior to gold sputter deposition, but little microstructural analysis has been made to complete the process-structure-properties relationship. Here, the grain size is shown to increase slightly but statistically significantly if an oxygen plasma etch and adhesion layer treatment of the film is performed prior to deposition of the gold. A log-normal grain size distribution is found for gold on each sample, and the grains are shown to be columnar. Gold deposited on non-treated polyimide shows a strong {111} texture, but a random texture is seen in both pretreated systems, indicating that the pretreatment affects the surface energy of the polyimide and alters the gold film growth.     

Laser-ablated plasma for deposition of ZnO thin films on various substrates

We report optical and structural properties of ZnO films deposited by pulsed laser deposition technique on 1100) n-typesilicon and quartz substrates at various pressures of back ground gas. ZnO plasma was created using KrF laser 1248 nm) atvarious pressures of the ambient gas, oxygen. Laser induced plasma at varying fluence on the target was investigated using optical emission spectroscopy and 2-D images of the expanding plumes. X-ray diffraction, atomic force microscopy, and spectro-photometry were used to characterize as grown films.     

Damage mode tensile testing of thin gold films on polyimide substrates by X-ray diffraction and atomic force microscopy

In situ tensile testing has been performed on thin gold film, 320 nm thick, deposited on polyimide substrates. During the tensile testing, strain/stress measurements have been carried out by X-ray diffraction using the d-sin²ψ method. The X-ray stress analysis suggests crack formation in the films for stresses greater than 670 MPa. The surface of the deformed specimen observed by atomic force microscopy (AFM) exhibits both cracks and two types of straight-sided buckling patterns lying perpendicular to the tensile axis. These buckling patterns can have a symmetrical or asymmetrical shape. The evolution of these two kinds of buckling structures under tensile stress has been observed in situ by AFM and compared to X-ray stress data. The results indicate that symmetrical straight-sided buckling patterns are induced by the compressive stress during unloading, whereas the asymmetrical result from the delamination of the film during the tensile deformation.     

Effect of a hard coat layer on buckle delamination of thin ITO layers on a compliant elasto-plastic substrate: An experimental–numerical approach

Layer buckling and delamination is a common interfacial failure phenomenon in thin film multi-layer structures that are used in flexible display applications. Typically, the substrate is coated on both sides with a hybrid coating, called a hard coat (HC), which acts as a gas barrier and also increases the scratch resistance. In this paper 250 nm thick indium tin oxide (ITO) layers have been deposited on a 200 μm thick high temperature aromatic polyester substrate (Arylite^TM), with and without a 3 μm HC. In order to study the influence of this HC layer on delamination phenomena, two-point bending experiments are performed from which buckle width and height values are measured after straightening of the sample. An analytical model and a finite element (FE) model are developed to estimate the adhesion properties from the measured buckle geometries. In the numerical model, the initiation and propagation of the delamination process is described by cohesive zone elements, of which the parameters are extracted from response surface model (RSM) results. Furthermore, the numerical model is used to illustrate the significant change in buckle geometry upon load reversal, i.e. from loaded to straightened state, which is governed by the elasto-plastic behavior of the substrate material. It is concluded that the addition of a HC layer significantly decreases the adhesion of the ITO layer. The latter is determined as function of the actual mode angle.     

A spectral scheme for the simulation of dynamic mode 3 delamination of thin films

Motivated by recent developments in laser-induced spallation testing of thin film structures, we develop a spectral scheme for the simulation of dynamic failure of thin films. In this first study, we focus on the anti-plane shear (mode 3) loading case. The scheme relies on an exact spectral representation of the elastodynamic solutions in the substrate and in the film, and their combination through interface conditions that involve general cohesive failure and/or frictional contact models. A detailed modal analysis of the response of a single spectral mode is performed to assess the stability and precision of the resulting numerical scheme. A set of dynamic fracture problems involving non-propagating and propagating cracks are simulated to show the ability of the numerical scheme to capture the effect of wave reflection on the near-tip stress and displacement fields, and on the dynamic motion of a crack along the film/substrate interface.     

Thermomechanical analysis of thin films on temperature-dependent elastomeric substrates in flexible heterogeneous electronics

Thermomechanical analysis is presented to study the basic temperature effects on elastomeric substrate of flexible electronics. Strains of a films-on-substrate structure related with three key temperatures are given based on the interfacial continuum model. An improved strain model is given and compared with other two models. The role of the temperature-dependent effects is highlighted and adopted to design a flexible inorganic/organic heterogeneous structure subject to little thermal action. The sensitivity analysis of three key temperatures is investigated, by which proper selection of technological parameter for poly(dimethylsiloxane) fabrication may be determined to eliminate the variation of stress of the interface in circumstances with temperature varying severely. This work contributes to systemic reliability and compatibility, structural design and thermal management of flexible electronics.     

Stress relief patterns of Co films deposited on circular silicone oil substrates

By using the expansive and mobile properties of silicone oil, circular liquid substrates with varied thicknesses naturally form on clean glass surfaces during deposition. Continuous cobalt (Co) films have been prepared on the circular liquid substrates by a direct current magnetron sputtering method, and the stress relief patterns of the Co films are investigated. The experiment shows that the Co film is susceptible to generating cracks due to thermal expansion of the silicone oil substrate during deposition. After deposition, subsequent cooling of the system creates a high compressive stress in the film, which is relieved by formation of various wrinkling morphologies. Based on the special growth mechanism and mechanical properties of the metal film deposited on a liquid substrate, the structural characteristics of the stress relief patterns and the underlying physical mechanisms are discussed in detail.     

A finite element model for the analysis of buckling driven delaminations of thin films on rigid substrates

The delamination process of thin films on rigid substrates is investigated. Such systems are typically subject to high residual compression and modest adhesion causing them to buckling driven blisters. In certain cases buckles with the shape of telephone cords are observed. A finite element model for quasi–static delamination growth is developed. Applying a Reissner–Mindlin shell kinematic for the film allows C ⁰− continuous shape functions. The traction vector at the film–substrate interface is obtained from the derivative of a cohesive free energy. Incorporation of loading and unloading conditions is considered for the irreversible process. The equilibrium state is computed iteratively in dependence of the compressive residual stresses. The computed telephone cord delaminations are stable asymmetric configurations whereas the symmetric configurations are unstable.