Effect of residual stress on delamination from interface edge between nano-films

The focus in this study is on the effect of residual stress on the delamination crack initiation from the interface edge between thin films, Cu/TiN, where the stress is intensified by the free edge effect. The delamination tests, where the mechanical stress is applied on the interface, show that the specimen with the thinner Cu film has an apparently higher strength at the interface edge. The residual stress in the films is then evaluated by curvature measurement of film/substrate coupon and the influence on the delamination is analyzed. The residual stress increases with the increase of film thickness and remarkably intensifies the stress near the edge. By superimposing the contributions of the applied load and the residual stress, a good agreement is obtained in the normal stress intensity near the interface edge at the delamination independent of the Cu thickness. This signifies that the combination of intensified stresses due to the applied load and the residual stress governs the crack initiation at the interface edge, and the toughness at the interface edge is evaluated by the stress intensity factor on the basis of the fracture mechanics concept.     

Role of plasticity on interface crack initiation from a free edge and propagation in a nano-component

In order to elucidate the role of plasticity on interface crack initiation from a free edge and crack propagation in a nano-component, delamination experiments were conducted by a proposed nano-cantilever bend method using a specimen consisting of ductile Cu and brittle Si and by a modified four-point bend method. The stress fields along the Cu/Si interface at the critical loads of crack initiation and crack propagation were analyzed by the finite element method. The results reveal that intensified elastic stresses in the vicinity of the interface edge and the crack tip are very different, although the Cu/Si interface is identical in both experiments. The plasticity of Cu was then estimated on the basis of the nano-cantilever deflection measured by in situ transmission electron microscopy. The plasticity affects the stress fields; the normal stress near the interface edge is intensified while that near the crack tip is much reduced. Both the elasto-plastic stresses are close to each other in the region of about 10 nm. This suggests that the local interface fracture, namely, the crack initiation at the interface edge and the crack propagation along the interface, is governed by elasto-plastic normal stress on the order of 10 nm.     

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.     

Reinvestigation of the effect of plasticity on delamination process of Si/Cu interface in a ductile nano-cantilever

Previous experimental investigations (Hirakata et al. Int J Fract 145:261–271, 2007) have demonstrated that Si/Cu/SiN/Pt/C nano-cantilever is delaminated along the interface between Cu and Si layers when subjected to monotonically bending load, and the measured load-displacement relationship shows a nonlinear behavior. Based on the continuum mechanics model, this study carries out numerical simulations on the crack nucleation and propagation along the Si/Cu interface in order to clarify the effect of plasticity on the fracture behavior of the ductile nano-component. Exponential type of cohesive zone model (CZM) combined with finite element method was adopted to characterize the constitutive relationship of the Si/Cu interface. Two sets of simulations are performed, i.e., Cu layer obeys either linear elastic or Ramberg–Osgood elasto-plastic constitutive relation. The characteristic parameters of interfacial adhesion are extracted through calibration via experimental results. The simulation results indicate that (i) cohesive strength and work of separation are the dominating CZM parameters, and the exponential CZM is suitable for describing the interfacial delamination between the Cu and Si film layers; (ii) the Cu film layer in this nano-cantilever more favorably obeys a linear elastic constitutive relation; (iii) comparing to bulk Cu, nano-scale Cu has a much higher yield stress and hardening rate, which leads to little plastic deformation of the nano-cantilever specimen during the entire delamination process. The numerical predictions are in good agreement with the experimental results, wherein brittle fracture occurred during the Si/Cu interfacial delamination. And the nonlinear load-displacement behavior observed by the tests may be due to the cohesive law of the Si/Cu interface, instead of the plastic deformation of the Cu film layer.     

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.     

Measurement of Interfacial Fracture Toughness of Surface Coatings Using Pulsed-Laser-Induced Ultrasonic Waves

This research develops a new technique for the measurement of interfacial fracture toughness of films/surface coatings using laser-induced ultrasonic waves. Using pulsed laser ablation on the bottom substrate surface, strong stress waves are generated leading to interfacial fractures and coating delamination. Simultaneously, a laser ultrasonic interferometer is used to measure the normal (out-of-plane) displacement of the top surface coating in order to detect coating delamination in a non-destructive manner. We can thus determine the critical laser energy for delamination, yielding the critical stress (that is, the interfacial strength). Subsequently, to examine the interfacial fracture toughness, additional pulsed laser irradiation is applied to a pre-delaminated specimen to show that the delamination area expands. This type of interfacial crack growth can be visualized using laser ultrasonic scanning. Furthermore, the calculation of elastic wave propagation was carried out using a finite-difference time-domain method) in order to accurately estimate the interfacial stress field. In this calculation, the stress distribution around the initial delamination is calculated to obtain the stress intensity factor. Based on the experimental and computational results, interfacial fracture toughness can be quantitatively evaluated. Since this technique relies on a two-laser system in a non-contact approach, it may be useful for a quantitative evaluation of adhesion/bonding quality (including both interfacial fracture strength and toughness) in various environments.     

Pre-cracking technique for fracture mechanics experiments along interface between thin film and substrate

Utilizing the difference in interface strength due to fabrication process, a technique for producing a sharp pre-crack between a thin film and a substrate is proposed. A cracked specimen for examining fracture toughness of interface between a sputtered copper (Cu) thin film and silicon (Si) is made by the method. A vacuum-evaporated Cu thin film, which has poor adhesion to Si, is inserted between the sputtered Cu thin film and the Si substrate as a release layer. The release layer debonds from the Si substrate at very low load, and the sharp pre-crack is successfully introduced along the interface. Using the pre-cracked specimen, the interface fracture toughness test is conducted and the critical J-integral, J_C, is evaluated as about 1 J/m² for the sputtered Cu/Si interface.     

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.     

Mixed mode fracture criterion of interface crack between dissimilar materials

This study presents an application of fracture mechanics to the interface crack between dissimilar materials. In this study, a concept of the stress intensity factors of an interface crack is discussed, and various types of specimens are tested experimentally for investigating the mixed mode fracture toughness criterion of an interface crack. The fracture toughness based on the stress intensity factors of an interface crack is decided by the fracture test and the boundary element analysis using the contour integral method. The mixed mode fracture toughness criterion is successfully characterized by the stress intensity factors of an interface crack.     

Mixed-mode interfacial fracture toughness for thermal barrier coating

A new interfacial fracture test method was developed for measuring the mixed-mode interfacial fracture toughness of thermal barrier coated material over a wide range of loading phase angles. The principle of this developed method is based on peeling the coating from the substrate due to compressive loading to the coating edge, as forming a shear loading to the interface, and slinging loading such as beam bending, as normal loading to the interface. The complete closed form of the energy release rate and associated complex stress intensity factor for our testing method is shown. An yttria stabilized zirconia (YSZ) coating, which was sprayed thermally on Ni-based superalloy, was tested using the testing device developed here.The results showed that the energy release rate for the coating-interfacial crack increased with loading phase angle, which is defined by tan⁻¹ for a ratio of stress intensity factor K₂ to K₁. It was noticed that the interfacial energy release rate increasing with mode II loading could be mainly associated with the contact shielding effect due to crack surface roughness rubbing together.     

Experimental investigation of interfacial fracture behavior in foam core sandwich beams with visco-elastic adhesive interface

Interfacial toughness as well as toughness enhancement and long term interfacial fracture behavior in sandwich beams were experimentally examined. The interfacial toughness was enhanced by inserting a chopped glass fiber mat at the interface during the fabrication process. Robust interfacial load capacity and improved toughness were obtained by the method. The long term interfacial fracture behavior presents the characteristics of the three-parameter solid (standard solid) model. The results of the long term fracture tests show a significant increment in crack opening displacement and nominal stress intensity factors. It indicates that during the process of structural design and analysis the interfacial fracture resistance may be overestimated without taking the visco-elastic effect of the materials of the structure into consideration.     

Internal hydrogen effects on thresholds for crack growth in the iron-based superalloy IN903

This study of internal hydrogen-induced crack growth in the iron-based superalloy IN903 shows that slow crack growth thresholds are significantly lower than fracture toughness values at the same prechargsd hydrogen concentrations. However, failure in all precharged samples occurred by slip band fracture which differed only in the extent of local surface plasticity. Quantitative fractography of these surface fracture features indicates that the crack tip hydrogen concentrations at threshold were higher than in fracture toughness samples. These higher concentrations are due to crack tip stress enhancement when sufficient time exists for hydrogen redistribution. In addition, continuum models based on mechanisms of failure demonstrate that the matrix carbides control crack growth susceptibility in slow crack growth and fracture toughness samples by establishing the characteristic distance that the crack tip stresses and strains must span to initiate fracture.     

Quantitative evaluation of the adhesion of metallic coatings using cylindrical substrate

This paper introduces an effective interfacial fracture toughness test based on interface fracture mechanics theory. This testing method uses a circumferentially notched tensile (CNT) specimen, which is ideally suited for determining the interfacial fracture resistance of coatings. Unlike other interfacial fracture tests, this test is simple to prepare, requires minimum test setup and is easy to model. An interfacial pre-crack was generated between a nickel coating and mild steel cylindrical substrate to evaluate adhesion strength. In situ acoustic and SEM analyses were used to determine the crack initiation or the critical load of failure. The critical energy release rate, critical stress intensity factors and phase angle were determined using the J integral which was determined by applying the critical load to the finite element model. A detailed finite element analysis was carried out to study the effect of different interface pre-crack positions and mode mixity on energy release rate for different notch angles and elastic modulus ratios. The cracking resistance of the interface was characterised by the notch angle of CNT specimens. The analysis showed an increase in interfacial fracture toughness as phase angle increases and was significant when the phase angle was large. The combined results of computational and experimental analysis showed that any defect or stress concentration at the interface could significantly weaken the adhesion of coating.     

Effects of stress on the interfacial reactions of metal thin films on (0 0 1)Si

The influences of stress on the interfacial reactions of Ti and Ni metal thin films on (0 0 1)Si have been investigated. Compressive stress present in the silicon substrate was found to retard significantly the growth of Ti and Ni silicide thin films. On the other hand, the tensile stress present in the silicon substrate was found to enhance the formation of Ti and Ni silicides. For Ti and Ni on stressed (0 0 1)Si substrates after rapid thermal annealing, the thicknesses of TiSi₂ and NiSi films were found to decrease and increase with the compressive and tensile stress level, respectively. The results clearly indicated that the compressive stress hinders the interdiffusion of atoms through the metal/Si interface, so that the formation of metal silicide films was retarded. In contrast, tensile stress facilitates the interdiffusion of atoms. As a result, the growth of Ti and Ni silicide is promoted.     

Numerical analysis of the stress–strain distributions in the particle reinforced metal matrix composite SiC/6064Al

The axisymmetric cell model consisting of interface, matrix and reinforced particle is used to simulate the tensile test of particle reinforced metal matrix composite for predicting the micro stress/strain field and macro tensile stress/strain curve. In simulation of the tensile test, the cohesive element model is selected to model interfacial crack growth. It mainly analyzed the effects of interfacial properties, reinforcement volume fractions and aspect ratios on the stress–strain states of particle reinforced metal matrix composite. The results show that the peak micro stress and plastic strain occur at the interface in which it is a certain angle from the tensile stress direction; with the interfacial fracture toughness and reinforcement volume fraction increasing, the flow stress increases firstly and then decreases. The tensile stress–strain properties of SiC/6064Al are good when the interfacial fracture toughness is equal to 60 J/m and the reinforcement fraction volume is equal to 20%. Smaller reinforcement aspect ratio leads to smaller micro stress in composites.     

Magnetically actuated peel test for thin films

Delamination along thin film interfaces is a prevalent failure mechanism in microelectronic, photonic, microelectromechanical systems, and other engineering applications. Current interfacial fracture test techniques specific to thin films are limited by either sophisticated mechanical fixturing, physical contact near the crack tip, or complicated stress fields. Moreover, these techniques are generally not suitable for investigating fatigue crack propagation under cyclical loading. Thus, a fixtureless and noncontact experimental test technique with potential for fatigue loading is proposed and implemented to study interfacial fracture toughness for thin film systems. The proposed test incorporates permanent magnets surface mounted onto micro-fabricated released thin film structures. An applied external magnetic field induces noncontact loading to initiate delamination along the interface between the thin film and underlying substrate. Characterization of the critical peel force and peel angle is accomplished through in situ deflection measurements, from which the fracture toughness can be inferred. The test method was used to obtain interfacial fracture strength of 0.8-1.9 J/m² for 1.5-1.7 μm electroplated copper on natively oxidized silicon substrates.     

In situ TEM observations of fracture in nanolaminated metallic thin films

Fracture of single crystal nanolaminated thin films has been investigated through in situ straining of cross-sectional samples of Cu/Ni nanolaminates grown on Cu (001) single crystal substrates. The earlest stages of deformation exhibits a confined layer slip mechanism. With continued straining, unstable fracture occurs creating a mixed-mode crack that propagates across the nanolaminate, roughly perpendicular to the interfaces. Eventually, stable crack growth with intense plastic deformation ahead of the crack tip occurs over many bilayers in the direction of crack growth. Simultaneously, plasticity was seen to spread only 1 or 2 bilayer distances normal to the crack, creating an extremely localized plastic zone. Transmission electron microscopic (TEM) examination after the test did not reveal the presence of dislocations in the crack wake, except where severe crack deflection was observed. By comparison, the plastic zone size in the substrate was greater by several of orders of magnitude.     

Cohesive zone criterion for cracking along the Cu/Si interface in nanoscale components

Crack initiation and propagation along the Cu/Si interface in multilayered films (Si/Cu/SiN) with different thicknesses of the Cu layer (20 and 200 nm) are experimentally investigated using a nano-cantilever and millimeter-sized four-point bending specimens. To examine the cohesive zone model (CZM) criterion for interfacial delamination along the Cu/Si interface in nanoscale stress concentration, an exponential type of CZM is utilized to simulate the observed delamination processes using the finite element method. After the CZM parameters for the Cu/Si interface are calibrated by experiment, interface cracking in other experiments is predicted. This indicates that the CZM criterion is universally applicable for describing cracking along the interface regardless of specimen dimensions and film thickness which include the differences in plastic behavior and residual stress. The CZM criterion can also predict interfacial cracking along Cu/Si interfaces with different stress singularities.     

Micromechanical analysis of fiber and titanium matrix interface by shear lag method

The model based on fracture mechanics is developed to evaluate the fracture toughness Γ of the fiber/matrix interface in titanium alloys reinforced by SiC monofilaments. Theoretical model for single fiber push-out testing is obtained by shear-lag method. The influences of several key factors (such as the applied stress needed for crack advance, crack length, and interfacial frictional shear stress) are discussed. Using the model, the interfacial toughness of typical composites including Sigma1240/Ti-6-4, SCS-6/Ti-6-4, SCS-6/Timetal 834, SCS-6/Timetal 21s, SCS-6/Ti-24-11 and SCS-6/Ti-15-3 are successfully predicted compared with previous results of these composites. It is verified that the model can reliably predict the interfacial toughness of the titanium matrix composites as well as other metal matrix composites, due to interfacial debonding usually occurs at the bottom face of the samples in such composites.     

混凝土/花岗岩界面Ⅰ-Ⅱ复合型动态断裂试验研究

为研究混凝土/岩石界面在复合型应力条件下的动态断裂性能,考虑四种应变率(10-5~10-2 s-1)及三种模态(21.8°,41.7°和60.3°)工况,对混凝土/花岗岩复合试件进行了四点剪切试验,获得了荷载与裂缝张开位移及裂缝剪切位移的关系曲线;结合界面力学理论和结构动力分析得到了界面Ⅰ型和Ⅱ型动态应力强度因子,据此得到并分析了断裂韧度、应变能释放率的率相关性及模态比相关性。结果表明:在所研究的应变率和模态角范围内,同一时刻的裂缝张开位移均大于裂缝剪切位移;Ⅰ型和Ⅱ型断裂韧度均随应变率的提高而增加,Ⅰ型断裂韧度随模态角的增大而减小,Ⅱ型断裂韧度随模态角的增大而增加;应变能释放率随应变率和模态角的增加均呈现出增长趋势。