An explicit elastic solution for a brittle film with periodic cracks

A two-dimensional explicit elastic solution is derived for a brittle film bonded to a ductile substrate through either a frictional interface or a fully bonded interface, in which periodically distributed discontinuities are formed within the film due to the applied tensile stress in the substrate and consideration of a “weak form stress boundary condition” at the crack surface. This solution is applied to calculate the energy release rate of three-dimensional channeling cracks. Fracture toughness and nominal tensile strength of the film are obtained through the relation between crack spacing and tensile strain in the substrate. Comparisons of this solution with finite element simulations show that the proposed model provides an accurate solution for the film/substrate system with a frictional interface; whereas for a fully bonded interface it produces a good prediction only when the substrate is not overly compliant or when the crack spacing is large compared with the thickness of the film. If the section is idealized as infinitely long, this solution in terms of the energy release rate recovers Beuth’s exact solution for a fully cracked film bonded to a semi-infinite substrate. Interfacial shear stress and the edge effect on the energy release rate of an asymmetric crack are analyzed. Fracture toughness and crack spacing are calculated and are in good agreement with available experiments.     

Influence of substrate compliance on buckling delamination of thin films

A thin film subject to in-plane compressive stress is susceptible to buckling-driven delamination. This paper analyzes a straight-sided delamination buckle with a focus on the effects of substrate compliance, following earlier work by B. Cotterell and Z. Chen. The critical buckling condition, the energy release rate and the mode mix of the interface delamination crack are calculated as a function of the elastic mismatch between the film and substrate. The average energy release rate at the curved end of a tunneling straight-sided blister is also determined. The more compliant the substrate, the easier for the film to buckle and the higher the energy release rates. The effect becomes significant when the modulus of the substrate is appreciably less than that of the film. When the substrate modulus is comparable to that of the film, or higher, the usual assumption is justified to the effect that the film is clamped along its edges. When the substrate is very compliant the energy release rate at the curved front exceeds that along the straight sides.     

An energy method to analyze through thickness thin film fracture during indentation

Nanoindentation was utilized to induce fracture of brittle thin oxide films on compliant substrates. The energies were calculated from integrating the resulting load-depth curves from indentation. The total energy applied to the system is a superposition of the energy to deform the substrate and the energy to fracture the film. The applied energy to deform the compliant substrate was separated from the energy applied to the film/substrate system resulting in the energy to fracture the film. The energy for fracture was then converted to a crack extension force and a stress intensity using linear elastic fracture mechanics. The toughness of thermally grown aluminum oxides is between 0.37 and 0.83 MPa m^0.5, and tends to decrease as film thickness increases over the range of 25 to 63 nm.     

Thin film and substrate cracking under the influence of externally applied loads

Cracking in thin film systems subject to residual tension is examined. The existing solution for the case of a crack tip in the substrate is modified to provide a solution of greater accuracy. The influence of external tensile loads on thin film and substrate cracking is examined. An approximate superposition scheme is presented for the determination of the energy release rate. Crack arrest is examined and parameters for determining the possibility of crack arrest are presented. For compliant films it was found that crack arrest does not occur when the substrate stress has the same magnitude as the residual stress. The influence of externally applied loads on crack channelling and conditions under which channelling will occur in the substrate are presented.     

A study towards improving mechanical properties of sol-gel coatings for polycarbonate

Scratch-resistant coatings based on 3-glycidoxypropyltrimethoxysilane and tetraethylorthosilicate with a cross-linking agent and different amounts of colloidal silica are prepared on polycarbonate substrates by sol-gel technique. The failure mode of this type of coating on soft plastic substrate under pencil scratch test is studied. It is found that the pencil scratch failure contains a gouge failure under the static pressure and a film cracking failure under the sliding of the pencil tip. The gouge failure is due to the early plastic deformation in the substrate, while the film cracking is due to the tensile stress in the film induced by the sliding and friction of the pencil tip. Factors influencing the static gouge failure and sliding cracking failure are investigated. It is found that the cross-linking agent and colloidal silica filler increase the intrinsic cross-linking, hardness, elastic modulus and fracture toughness of the coating material, therefore, reduce the film cracking tendency; whereas the increased layer thickness and multi-layer coating improve the pencil scratch resistance significantly via delayed plastic deformation in the substrate. Based on these analyses, we conclude that the main factors towards improved pencil scratch resistance are: layer thickness, elastic modulus, fracture toughness and intrinsic hardness of the coating material. Pencil hardness is increased from grade 2B to 5H by adjusting these parameters.     

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.     

Processing and properties of electrodeposited layered surface coatings

Abstract

Hard chromium, produced by conventional direct current (DC) electrodeposition, cannot be deposited to thicknesses greater than about 5μm because of the buildup of processing stresses which cause channel cracks in the coating. Much thicker chromium coatings may be produced by depositing a layered structure using alternate DC plating and periodic current reversal (PR). Such layering produces a through thickness stepped gradient in residual stresses. Most importantly, a bending moment develops in the coating whenever the substrate is compliant. For thin, compliant substrates, the coating cracks and spalls off early on. For thick, non-compliant coatings, much thicker coatings can be formed. Fracture resistance must be considered in relation to both specimen and loading geometries. Since the inherent bending moment causes a maximum tensile stress at the coating surface, the loading geometry is almost always analogous to bending, and fracture resistance is provided through deviation of the channel crack by weak interfaces, resulting in ‘terrace cracking’.     

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.     

A numerical study of contact damage and stress phenomena in curved porcelain/glass-filled polymer bilayers

Finite Element Analysis is used to examine contact damage induced by Hertzian indentation of a porcelain coating on a glass-filled polymeric substrate. Different forms of cracking in the porcelain coating are studied –“Hertzian” cone cracks close to the indenter, more distant “outer” cone cracks, and “radial” cracking at the coating/substrate interface. The effects of porcelain coating thickness and radius of curvature on the critical stresses for initiation of these cracks are examined. The predicted critical load curves suggest that for systems with compliant substrates (relative to the coating) with a given radius of curvature, there is an optimum porcelain coating thickness that maximises the critical load for cone cracking. Conversely, for a given coating thickness, the effects of curvature vary significantly – for thinner coatings, where outer cone cracks are dominant, highly convex surfaces are more resistant to cracking, whereas for thicker coatings, which are more prone to Hertzian cone cracking, concave surfaces produce a higher predicted critical load. Curvature is observed to have little effect on the critical load for the formation of radial cracks, which remains the dominant mode of failure in cases of thin coatings on compliant substrates.     

Mechanical integrity of thin inorganic coatings on polymer substrates under quasi-static, thermal and fatigue loadings

The interplay between residual stress state, cohesive and adhesive properties of coatings on substrates is reviewed in this article. Attention is paid to thin inorganic coatings on polymers, characterized by a very high hygro-thermo-mechanical contrast between the brittle and stiff coating and the compliant and soft substrate. An approach to determine the intrinsic, thermal and hygroscopic contributions to the coating residual stress is detailed. The critical strain for coating failure, coating toughness and coating/substrate interface shear strength are derived from the analysis of progressive coating cracking under strain. Electro-fragmentation and electro-fatigue tests in situ in a microscope are described. These methods enable reproducing the thermo-mechanical loads present during processing and service life, hence identifying and modeling the critical conditions for failure. Several case studies relevant to food and pharmaceutical packaging, flexible electronics and thin film photovoltaic devices are discussed to illustrate the benefits and limits of the present methods and models.     

Evaluation of thin film adhesion to a compliant substrate by the analysis of progressive buckling in the fragmentation test

The interface toughness of a thin coating/compliant substrate system is estimated based on the evolution of coating buckle patterns in the fragmentation test. The linear density of coating buckles as a function of applied strain is determined experimentally for a SiO_x coating deposited on a polyethylene terephthalate film. A three-dimensional non-linear finite element model is developed to simulate the process of buckle formation in a single narrow coating strip. The elastic energy released during buckling-driven delamination is obtained from the energy balance in the system before and after the buckling event. Both the interface adhesion and the total energy release rate, which includes the plastic dissipation in the substrate during debonding, are evaluated. The apparent interfacial toughness, equal to 15 J/m² at the onset of buckling, is found to increase with strain. This is tentatively explained by the probabilistic features of the buckle accumulation process, reflected also in the random locations of buckles evolving towards a log-normal distribution of buckle spacings at high strains.     

Channel cracking during thermal cycling of thin film multi-layers

This paper describes mechanisms that can lead to film channel cracking, even in scenarios when layer thickness is small. Computational models are used to illustrate conditions that lead to the introduction of channel cracks and their subsequent cycle- or time-dependent propagation. Results for elastic structures with periodic features are briefly reviewed to illustrate that small low-modulus sections promote cracking in adjacent layers because they allow for the release of strain energy in adjacent sections with high residual stress. Inelastic deformation in layers adjacent to the cracked layer may also act to increase the channel crack driving force, by allowing for increasing displacements that serve to release strain energy. Two inelastic mechanisms form the primary focus in this effort: rate-independent plasticity and creep. Analyses of a cracked film on an elastic-plastic layer reveal pronounced cyclic displacements (as known as ratcheting) when the misfit thermal strain amplitude in the ductile layer exceeds twice its yield strain. Similar behavior occurs in cracked films on layers susceptible to creep. Simulations are presented for both isolated cracks and periodic arrays of cracks, and illustrate that the likelihood of cracking grows dramatically with time. In both inelastic regimes, the upper limit on deformation is dictated by the residual stress in the elastic layer and the substrate dimensions. These results are discussed in the context of analytical models developed elsewhere and potential experiments.     

Delaminating buckling model based on nonlocal Timoshenko beam theory for microwedge indentation of a film/substrate system

A novel model built on the basis of nonlocal Timoshenko beam theory is presented for delaminating buckling in the microwedge indentation test of a thin film on an elastic substrate. Two size effects are accounted for in the proposed model. One is the delamination size effect, and the other is the film thickness effect. The influence of the elastic deformation in the substrate and the indentation-induced impression or notch on the buckling behaviors are taken into consideration by employing coupled line springs as the boundary conditions of the buckled film. The critical stress for buckling, the energy release rate and the phase angle of the interface delamination crack are calculated and compared with those by classical beam theories. Sensitivity of the two size effects is observed.     

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.     

Mechanics of tunnelling cracks in trilayer elastic materials in tension

In this work, the crack driving force for a tunnelling crack in a thin brittle layer confined by dissimilar thick, and more compliant, elastic layers is considered at tensile loading. The steady-state energy release rate is evaluated using distributed dislocation technique and series representation of the complex potentials for an isotropic trimaterial. Evolution of the energy release rate with the crack length is studied by means of FEM. The 3D FEM simulations for tunnel cracks suggest that the ERR can represented by a universal relation (mastercurve) in suitably normalised co-ordinates. An analytical approximation of the ERR mastercurve is obtained as a function of crack length, cracking layer thickness, and a non-dimensional steady-state ERR.     

The propagation of cracks and crack-like defects in thin adhered polymer films

The strain energy release rateG of a through-thickness crack in a thin film that adheres to a rigid substrate is shown to vary linearly with the film thickness at constant film stress.G is normally small, so adhered polymer films are only expected to crack in the presence of an aggressive environmental agent unless the polymer is very brittle. A minimum film thickness for cracking is likely to be observed. The propagation of crack-like defects in a polyimide in the presence of xylene was examined experimentally. The defects grew at a constant rate (independent of their length) that increased rapidly with film thickness. The minimum film thickness for defect growth was found to be about 2m.     

Dimensional control of brittle nanoplatelets. A statistical analysis of a thin film cracking approach

Nanoparticles are essential building blocks for nanotechnology. In this paper we demonstrate a novel method to create nanoplatelets by thin film cracking. The thickness of the resulting platelets is determined by the film thickness, and their aspect ratio is controlled by the total strain and the elastic mismatch between substrate and thin film. Platelets can be created from any brittle film independently of microstructure and materials class. The feasibility of this method is substantiated by a statistical analysis of the fracture process.     

Delamination of thin film strips

Delamination of residually stressed thin film strips is analyzed to expose the dependence on strip width and film/substrate elastic mismatch. Isotropic films and substrates are assumed. The residual stress in the film is tensile and assumed to originate from mismatch due to thermal expansion or epitaxial deposition. Full and partial delamination modes are explored. In full delamination, the interface crack extends across the entire width of the strip and releases all the elastic energy stored in the strip as the crack propagates along the interface. The energy release rate available to propagate the interface crack is a strong function of the strip width and the elastic modulus of the film relative to that of the substrate. The energy release rate associated with full delamination is determined as a function of the interface crack length from initiation to steady-state, revealing a progression of behavior depending in an essential way on the three dimensionality of the strip. The dependence of the energy release rate on the remaining ligament as the interface crack converges with the strip end has also been calculated, and the results provide an effective means for inferring interface toughness from crack arrest position. A partial delamination propagates along the strip leaving a narrow width of strip attached to the substrate. In this case, the entire elastic energy stored in the strip is not released because the strain component parallel to the strip is not relaxed. A special application is also considered, in which a residually stressed metal superlayer is deposited onto a polymer strip. The energy release rate for an interface crack propagating along the interface between the polymer and the substrate is determined in closed form.     

基于薄膜SOI材料的GaN外延生长应力释放机制

本文研究了SOI衬底上采用MOCVD方法生长GaN材料的应力释放机制.采用SIMOX工艺制备的具有薄膜顶层硅的SOI材料作为外延生长的衬底材料,采用MOSS在位检测系统以及拉曼测试作为GaN内部应力的表征手段.结果表明,SOI材料对硅基GaN异质外延中的晶格失配应力和热应力的释放都有显著作用.薄膜SOI材料通过顶层硅与外延层的界面滑移,将一部分晶格失配应力通过界面的滑移释放,并且通过柔性薄膜顶层硅自身的应力吸收作用,将一部分热失配应力转移到衬底,从而有效地降低了GaN外延层的张应力.