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.     

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.     

Interaction between matrix cracking and edge delamination in composite laminates

Matrix cracking and edge delamination are two main damage modes in continuous-fibre composite laminates. They are often investigated separately, and so the interaction between two damage modes has not yet been revealed. In this paper, a simple parallel-spring model is introduced to model the longitudinal stiffness reduction due to matrix cracking and edge delamination together. The energy release rate of edge delamination eliminating the matrix crack effect and the energy release rate of matrix cracking in the presence of edge delamination are then obtained. Experimental materials include carbon- and glass-fibre-reinforced bismaleimide composite laminates under static tension. The growth of matrix cracks and edge delaminations was recorded by means of NDT techniques. Results show that matrix cracks may initiate before or after edge lamination. This depends on the laminate layup, and especially on the thickness of the 90° plies. Edge delamination may also induce matrix cracking. Matrix cracking has a significant effect on the stiffness reduction in GRP laminates. The present model can predict the stiffness reduction in a laminate containing both matrix cracks and edge delaminations. The mixed-mode delamination fracture toughness obtained from the present model shows up to 50% differences compared with O'Brien's model for GRP laminates. However, matrix cracking has a small effect on the mixed-mode interlaminar fracture toughness of the CFRP laminates.     

Crack patterns in brittle thin films

The physical system studied is a brittle elastic film bonded to an elastic substrate with different elastic properties; a residual tensile stress is presumed to exist in the film. The focus of the study is the influence of the mismatch in elastic properties on patterns of crack formation in the film. The stress intensity factor and crack driving force for growth of a periodic array of cracks in the direction normal to the interface under two-dimensional conditions are determined for any crack depth and any mismatch in elastic parameters. It is found that, even for a relatively stiff film material, the stress intensity factor of each crack as a function of crack depth exhibits a local maximum. The driving force for crack extension in the direction parallel to the interface is then determined on the basis of these two-dimensional results, and the equilibrium spacing of crack arrays is estimated for given residual stress. The results of the calculations are used as a basis for qualitative arguments to explain the crack patterns which have been observed in GaN films on Si substrates.     

Crack patterns in brittle thin films

The physical system studied is a brittle elastic film bonded to an elastic substrate with different elastic properties; a residual tensile stress is presumed to exist in the film. The focus of the study is the influence of the mismatch in elastic properties on patterns of crack formation in the film. The stress intensity factor and crack driving force for growth of a periodic array of cracks in the direction normal to the interface under two-dimensional conditions are determined for any crack depth and any mismatch in elastic parameters. It is found that, even for a relatively stiff film material, the stress intensity factor of each crack as a function of crack depth exhibits a local maximum. The driving force for crack extension in the direction parallel to the interface is then determined on the basis of these two-dimensional results, and the equilibrium spacing of crack arrays is estimated for given residual stress. The results of the calculations are used as a basis for qualitative arguments to explain the crack patterns which have been observed in GaN films on Si substrates.     

Straight-sided, buckling-driven delamination of thin films at high stress levels

The fracture mechanics of a straight-sided, thin film delamination at stress levels, which are high compared to the stress required to initiate the delamination is investigated. Buckling at a bifurcation point of the delaminated region, resulting from incompletely relieved stresses in this region, is analysed by a semi- analytical approach for delaminations of infinite extent. The results are compared to numerical predictions based on finite element calculations for finite sized delaminations. The finite element calculations are carried out in the post-buckling regime showing that parts of the crack front will close as a result of bifurcation buckling, while other parts will experience enhanced energy release rate and mode I stress intensity factor. The mode III stress intensity factor is shown to be negligible at the stress levels analysed.     

Interaction between thin indium films and single-crystal ZnAs2 substrates

X-ray photoelectron and Auger electron spectroscopic studies of In/ZnAs₂ structures revealed a chemical reaction at the film-substrate interface at substrate temperatures between 400 and 650 K. Gibbs energy calculations showed that the more likely products of the interfacial reaction are InAs and Zn₃As₂.     

Finite element analysis of interface delamination and buckling in thin film systems by wedge indentation

A finite element method is used to study the interface delamination and buckling of thin film systems subject to microwedge indentation. In the formulation, the interface adjoining the thin film and substrate is assumed to be the only site where cracking may occur. Both the thin film and the substrate are taken to be ductile materials with finite deformation. A traction-separation law, with two major parameters: interface strength and interface energy, is introduced to simulate the adhesive and failure behaviors of the interface between the film and the substrate. The effects of the interface adhesive properties and the thickness of the thin film on the onset and growth of interface delamination and the film buckling are investigated.     

A non-contact, thermally-driven buckling delamination test to measure interfacial fracture toughness of thin film systems

Interfacial fracture toughness measurements of thin film-substrate systems are of importance in many applications. In the microelectronics industry, the interfacial adhesion between the dielectric-barrier-metal layers on a semiconductor chip is critical for chip reliability. In this paper, we propose a thermally-driven patterned buckling delamination test that does not use a pre-existing weak interface. The test relies on causing a patterned film to debond from its substrate by inducing a compressive stress due to heating of the film on a thick silicon substrate. The compressive stress causes the film to buckle and debond from the substrate. A model for the propagation of the buckling-induced debond is then developed to estimate interfacial fracture toughness. The efficacy of the thermally-driven buckling test is demonstrated on a model Al/SU8/Si film-substrate system wherein the Al film debonds along its interface to SU8. The interfacial toughness of the Al/SU8 interface is estimated using the proposed test and is compared to the toughness for the same system obtained using an alternative test with a weakened interface to validate the developed elastic-plastic model for buckling-induced debond propagation.     

Edge delamination of residually stressed thin films: viscoelastic effects

The theory of interfacial delamination governed by the critical energy release rate criterion is used to predict the initiation of crack growth in thin polyimide films bonded to elastic substrates. The elastic solution for thin films is extended to the viscoelastic case using a correspondence principle valid to the point of initiation of crack growth. A tentative model for decohesion under moisture cycling is proposed to model delayed failure due to exposure to ambient humidity. The effects of relevant parameters such as film thickness and relative humidity are shown for a PMDA/ODA polyimide film bonded to glass.     

Overall elastic domain of thin polysilicon films

We present a numerical study aimed to define the overall elastic domain of thin polysilicon films subjected to in-plane loadings. Homogenized properties are obtained for digital polycrystalline microstructures, generated in a representative volume element (RVE) through Voronoi tessellations. To locate the elastic limit, three micromechanical sources of dissipation are allowed for: (i) trans-granular cracking, as due to tensile stresses attaining the local strength inside silicon grains; (ii) inter-granular failure, as due to coupled normal-shear tractions attaining a local effective strength along grain boundaries; (iii) trans-granular phase transformation, as due to compressive stresses attaining a critical threshold inside silicon grains.Results of the homogenization procedure show that Rankine-type overall domains are too crude approximations to the polysilicon elastic envelope, since corners arise because of switching among the three dissipative modes allowed for. Outcomes of the analysis allow also to estimate the size of the RVE required to get objective overall polysilicon properties: according to data already available in the literature, it is shown that the RVE has to gather at least a few hundreds of grains.     

On size effect of cleavage cracking in polycrystalline thin films

A crack trapping model is developed for the fracture resistance of high-angle grain boundaries in free-standing brittle thin films, based on which a new size effect is predicted. In addition to the crystallographic misorientations, the grain boundary toughness is also dependent on the film thickness, primarily due to the geometrically necessary crack front branching.     

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.     

Effects of substrate compliance on circular buckle delamination of thin films

The present work analyzes circular delamination buckling in a film/substrate system based on the Von Karman nonlinear plate theory with the consideration of elastic deformation of the substrate. Due to the axisymmetry of circular buckling, the substrate deformation is modeled by coupled springs and the spring compliances are determined from the dimension analysis and finite element calculations. The numerical shooting method is used to solve the nonlinear post-buckling problem. The stress intensity factors, the energy release rate, and the phase angle are given here for a variety of the elastic mismatch between the film and the substrate. The results show that in some cases, the energy release rate can be several times larger than that derived from the widely used clamped edge condition.     

Effect of substrate roughness on the contact damage of thin brittle films on brittle substrates

The effect of substrate and surface roughness on the contact fracture of diamond-like carbon coatings on brittle soda-lime glass substrates has been investigated. The average surface roughness (R_a) of the examined samples ranged from 15 nm to 571 nm. Contact damage was simulated by means of spherical nanoindentation, and fracture was subsequently assessed by focused ion beam microscopy. It was found that, in the absence of sub-surface damage in the substrate, fracture occurs in the coating in the form of radial, and ring/cone cracks during loading, and lateral cracks during unloading. Increasing the surface roughness results in a decrease in the critical load for crack initiation during loading, and in the suppression of fracture modes during unloading from high loads. When sub-surface damage (lateral cracks) is present in the substrate, severe spalling takes place during loading, causing a large discontinuity in the load-displacement curve. The results have implications concerning the design of damage-tolerant coated systems consisting of a brittle film on a brittle substrate.     

The surface effect on the strain energy release rate of buckling delamination in thin film-substrate systems

Gurtin-Murdoch continuum surface elasticity model is employed to study the buckling delamination of ultra thin film-substrate system. The effects of surface deformation and residual stress on the large deflection of ultra thin film are considered in analysis. A concept of effective bending rigidity (EBR) for ultra thin plate is proposed on the basis of Gurtin-Murdoch continuum theory and the principle of minimum potential energy. The governing equations with EBR are formally consistent with the classical plate theory, including both small deflection and large deflection. A surface effect factor is introduced to decide whether there is need to consider the surface effect or not. Combining the buckling theory and interface fracture mechanics, we obtain analytical solutions of the critical buckling load and the energy release rate of the interface crack in the film-substrate system. It is seen that the surface deformation and residual stress have significant effects on the buckling delamination of ultra thin film-substrate system.     

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.     

A simple model for elastic fracture in thin films

A simple model for the cracking of thin films has been developed and investigated. The film is represented by a network of bonds and nodes which initially form a triangular lattice in which each node is at the junction of six bonds. The nodes are also attached to a rigid substrate by bonds which are not broken but have a relatively small force constant. Cracking is simulated by a sequence of thermally activated bond breaking events followed by mechanical relaxation. If the stretching force constant associated with the bonds in the surface layer is large, linear cracks propagate rapidly and, at a later stage, are connected by secondary cracks which become less and less linear as the strain in the surface layer is relaxed by the cracking process. Many of our simulations exhibit a distint “initiation” period in which the bond breaking rate is low, followed by a period of rapid crack propagation in which a large fraction of the surface strain energy is released. This period is then followed by a second period of relatively slow bond breaking. During the first period isolated defects are formed, followed by linear cracks in the second period. During the third period non-linear cracks connect the linear cracks, and structures which resemble shear bands are formed. Results for the effects of finite relaxation rates for the elastic network (visco-elastic effects) are also presented.     

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.     

Surface effects on delamination of a thin film bonded to an elastic substrate

The delamination of a circular thin film at micro/nanoscale is studied using the Kirchhoff plate theory incorporating surface effects in this paper. Bending of a clamped circular nanoplate subjected to a concentrated force at the center or a uniformly distributed force over a lateral surface is solved. The bending deflection is derived in closed form. The adhesion energy and its release rate for delamination are determined when surface effects are taken into account. The influences of surface residual stress and surface elasticity along with the film’s size on the energy release rate of debonding advance or interfacial adhesion of a thin film bonded to an elastic substrate are analyzed for applied loading or given displacements. Analytic results are compared with experimental data and satisfactory agreement is confirmed.