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.     

The role of flaw geometry in thin film delamination from two-dimensional interface flaws along free edges

Delamination from planar interface edge flaws between a thin film and a semi-infinite substrate is examined to determine the roles of flaw width and depth relative to the film thickness. The flaws have curved and straight sections, and the crack front intersects the free edge at a right angle. Three-dimensional finite element models are used to extract local energy release rates and mode-mixity angles along the entire crack front. This paper focuses the crack dimensions required to reach steady state, wherein energy release rates are independent of flaw dimensions along the entire crack front. Results indicate that moderate elastic mismatch, although affecting mode mixity, plays a small role in determining the crack aspect ratios required to reach steady state. For wide cracks, the energy release rate for crack advance into the film interior approaches the plane-strain steady-state value when the half-width of the crack is approximately four times its depth (for cracks whose depths is several times the film thickness). For narrow cracks, the energy release rate near the free edge is significantly greater than the plane-strain steady-state result, and reaches a steady state when the depth approximately 10 times its width (for widths several time the film thickness). The results imply that delamination from wide cracks is reasonably accurately predicted via plane-strain analyses. Conversely, two-dimensional models are incapable of accurately predicting delamination from narrow cracks, which have a tendency to widen into flaws with more balanced aspect ratios (i.e. without growth in the depth direction).     

Delamination of Thin Films From Two-Dimensional Interface Flaws at Corners and Edges

This paper details the mechanics governing delamination of thin films driven by thermal expansion mismatch from two-dimensional interface flaws. Two scenarios are considered: (i) the edge of the film is concurrent with the edge of the substrate and (ii) the substrate extends past the edge of the film. Fully three-dimensional finite element models are used to analyze semi-circular interface flaws (along the edge) or quarter-circle interface flaws (at the corner of the film) for both scenarios. Results are presented for energy release rates and mode-mixity along two-dimensional crack fronts. For all cases considered, the crack driving force very close to the intersection of the crack front and the edge of the film is substantially larger than that for the interior portions of the crack front. For a given flaw size, the energy release rate along the entire front is higher when the substrate extends past the end of the film. The stress intensity factors are mixed-mode along the entire crack front; the predictions illustrate that the mode III component comprises a substantial contribution to the crack driving force over a significant part of the crack front. The implications of the results on film delamination is discussed in terms of critical flaw sizes, crack front profiles and the influence of the intersection singularity.     

Vapor Pressure and Residual Stress Effects on Mixed Mode Toughness of an Adhesive Film

Temperature- and moisture- induced delamination leading to popcorn package cracking is a major package reliability issue for surface-mount plastic encapsulated microcircuits (PEM). Crack propagation along one of the interfaces of a ductile adhesive joining two elastic substrates is modeled to study interface delamination and toughness of PEMs. The polymeric adhesive is stressed by remote loading and residual stress. Along the crack front, the film-substrate interface is modeled by a strip of cells that incorporates vapor pressure effects on void growth and coalescence through a Gurson porous material relation. Results show that under high levels of vapor pressure, increasing film thickness will produce smaller enhancement on the steady-state fracture resistance of the interface, also referred to as the joint toughness. Across all mode mixity levels, vapor pressure effects dominate over residual stress. The adverse effects of vapor pressure are greatest in highly porous adhesives subjected to a strong mode II component. The latter is representative of the likely state of loading in IC packages since residual stress, resulting from the film-substrate thermal mismatch, induces a predominantly mode II component.     

Interfacial crack propagation in a thin viscoelastic film bonded to an elastic substrate

Edge decohesion along the interface of a thin viscoelastic film bonded to an elastic substrate under tensile residual stresses is considered. The tensile residual stress in the film is replaced by a combination of edge loads, and an explicit relation of strain energy with respect to time is obtained through simple beam analysis. The strain energy function is discretized into time steps which are assumed to be very small so that the dissipation effects over the time steps can be neglected. The energy release rate is then calculated using a Griffith type energy balance. An analytical model is developed to predict the crack growth and its velocity. Extent of crack growth along the interface is prediced based on a fracture criteria. The analytical predictions are compared with results from a viscoelastic finite element analysis.     

Fixtureless superlayer-driven delamination test for nanoscale thin-film interfaces

A fixtureless delamination test has been developed to measure the interfacial fracture toughness of patterned nanoscale thin films on a substrate. The driving energy for delamination propagation is supplied by a highly stressed superlayer deposited on top of the nanoscale thin film. The amount of energy available for delamination propagation is changed by depositing an etchable thin release layer with varying width between the nanoscale thin-film strip and the substrate. By designing a decreasing area of the release layer, it is possible to arrest the delamination at a given location, and the interfacial fracture toughness or critical energy release rate can be found at the location where the delamination ceases to propagate. For titanium film with a thickness of 90 nm, the results show that the interfacial fracture toughness of titanium/silicon ranges from 3.45 J/m² to 5.70 J/m² when the mode mixity increases from 6.8° to 38.4°. The methodology presented in this paper is generic in nature, and can be used to measure the process-dependent interfacial fracture toughness of various micro and nanoscale thin films on a substrate.     

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.     

An interface crack between an orthotropic thin film and substrate

This work is concerned with a semi-infinite interface crack between a thin film and a substrate. The two materials are assumed to be linearly elastic and orthotropic. A solution is presented for the stress field due to an edge dislocation on the interface which is valid for any combinations of material parameters. It is found that the behavior of such a bi-material system is governed by 6 independent material parameters. The stress intensity factor is computed for general edge loadings by solving integral equations numerically, and the size of the K-dominant zone is also studied for a residually stressed thin film. The situations in which the K-field zone of dominance is very small are identified and discussed.     

Edge delamination in an orthotropic bimaterial consisting of a thin film and a substrate

This paper investigates edge delamination in an orthotropic layered structure composed of a thin film and a substrate under a temperature change. An edge interface crack is analyzed for two configurations in which it emerges from an interior or corner edge of the film. Special attention is paid to the effects of orthotropic material constants on delamination cracking. The necessary material parameters involved in the energy release rate and mode mixity for the interface crack are found based on a modified Stroh formalism. The explicit dependence of the energy release rate and mode mixity on one orthotropic parameter for the film is discovered using an orthotropy rescaling technique. The effects of other material parameters on the energy release rate and mode mixity are examined numerically, and the growth and arrest of edge interface cracks are discussed based on an energy criterion.     

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.     

Crack initiation at free edge of interface between thin films in advanced LSI

Since electronic devices are made of multi-layered sub-micron films, delamination along the interface is one of the major failure mechanisms. This paper aims to develop a method for evaluating the mechanical criterion of interface cracking between thin films on a substrate. The focus is put on crack initiation from the free edge of the interface where the stress concentrates due to the mismatch of elastic deformation. In the evaluation, it is important to exclude plastic deformation and fracture of the thin metal film, because they bring about ambiguity on the measured magnitude of interface strength. In this study, an experimental method is proposed on the basis of fracture mechanics concepts, and the validity is examined by tests on Cu (conductor metal)/TaN (barrier metal) interface in a large-scale integrated circuit. The critical stress intensity at delamination crack initiation is successfully analyzed by the boundary element method.     

Three-dimensional finite element analysis of fracture modes for the pull-off test of a thin film from a stiff substrate

A three-dimensional geometrically nonlinear finite element analysis model is presented to study the interfacial delamination for the pull-off test of a thin film strip debonded from a stiff substrate. The strain energy release rates of all three modes (mode I, mode II, and mode III) along the debond front are considered and calculated to investigate the mixed fracture modes for the entire deformation regime from bending plate to stretching membrane. These results indicate that the individual strain energy release rates and the total energy release rate vary along the width of the debond front and strong three-dimensional edge effects exist near the free edges of the film. Interestingly, residual stress also plays an important role in controlling mixed fracture modes and the variation of the energy release rates. Finally, the three-dimensional finite element model is compared with an analytical solution developed earlier. The three-dimensional finite element model is found to provide additional insights for interfacial delamination for the pull-off test.     

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.     

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.     

Scale effects in the initiation of cracking of a scarf joint

The singular stress field at the interface-corner of a bi-material scarf joint is analysed for a strip of finite width, w, under remote tension and bending. The two substrates are taken as linear elastic and isotopic. The intensity of the singular stress field is calculated using a domain integral method, and is plotted as a function of joint geometry and material mismatch parameters. It is envisaged that the intensity of singularity can serve as a valid fracture criterion provided the zone of nonlinearity is fully embedded within the singular elastic field. It is assumed that fracture initiates when the magnitude of the corner singularity attains a critical value; consequently, the fracture strength of the joint depends upon the size of the structure. In addition, the interfacial stress intensity factor and the associated T-stress are determined for an edge interfacial crack. When the crack is short with respect to the width of the strip, the stress intensity factor is dominated by the presence of the corner singularity; a boundary layer formulation is used to determine the coupling between the crack tip field and the interface-corner field. The solution suggests that an interfacial crack grows unstably with a rapidly increasing energy release rate, but with only a small change in mode mix. This revised version was published online in July 2006 with corrections to the Cover Date.     

Delamination of layered structures on elastic foundation

This study presents an interface fracture mechanics analysis of delamination of a layered beam resting on a Winkler elastic foundation subject to general mechanical loads. A crack tip element on elastic foundation model is established first, through which, two concentrated forces existing at the crack tip are determined in closed-form. Then total energy release rate of the crack can be expressed in term of these two forces. By using available numerical results in the literature, the phase angle of the total energy release rate is also obtained. To verify the validity and accuracy of the solutions, debonding of a bonded overlay from the base structure resting on a Winkler elastic foundation is analyzed using the present solution. Comparisons with the baseline results obtained by finite element analysis suggest that the present analytical solution provides an excellent estimation of the total energy release rate and its phase angle for interface cracks in layered structure on elastic foundation. This study provides an approximated analysis of the debonding of a thin overlay debonding from the concrete pavement, where the effect of the base structure is simplified by a Winkler elastic foundation. This solution can also be used to analyze other similar delamination problems, such as local delamination in laminated composites, and face sheet delimitation in sandwich beams.     

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.     

Investigation on the fatigue crack behavior of Zr702/TA2/Q345R composite plate with a crack normal to interface

In this paper, the effects of maximum load, load ratio, and average load on fatigue crack propagation of Zr702/TA2/Q345R composite plate with a crack normal to the interface are studied by experiment and finite element method. When crack propagates to the interface from the compliant material side, the crack growth rate decreases to the minimum at first. After crack penetrates through the interface, the fatigue crack growth rate accelerates continuously. When crack propagates to the interface from the stiff material side, the fatigue crack growth rate generally increases with the crack length. Regardless of the direction of crack growth, the increase of load ratio will weaken the difference of crack growth rate near the interface caused by material property mismatch. Finite element results show that elastic modulus mismatch significantly changes the variation of the stress intensity factor amplitude. All results demonstrate that crack growth rate is dependent on the competition of the stress intensity factor amplitude, the fatigue crack growth rate in the corresponding material, and the interface strength.