Mechanical and thermal properties of physical vapour deposited alumina films Part II Elastic, plastic, fracture, and adhesive behaviour

Two mechanical characterization techniques were used to deduce the elastic, plastic, fracture, and adhesive properties of non-reactive physical vapour deposited alumina films of varying thickness on Al₂O₃-TiC substrates deposited at two different substrate biases. Depth-sensing indentation at both nano- and macroscopic load scales was used to determine the elastic and plastic properties of the films. Gravity-loaded Vickers indentation was performed to examine the fracture properties of the film and of the interface. Novel fracture mechanics models were developed to describe indentation-induced film fracture by channel cracks and indentation-induced interface delamination. The former model was used to determine the film toughness and the latter model was used to deduce the interfacial fracture resistance of the films and correctly predicted the effect of changing film thickness. Both models described the measured crack lengths with indentation load well and were used to identify the transition from radial and lateral cracking to channel and interfacial cracking.     

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.     

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.     

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.     

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.     

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.     

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.     

Hybrid spectral/finite element analysis of dynamic delamination of patterned thin films

A combined spectral and finite element analysis is performed to investigate the dynamic edge delamination of patterned thin films from a substrate. The analysis is motivated by an emerging experimental technique in which high-amplitude laser-induced stress waves initiate progressive interfacial debonding of thin film interfaces. The numerical method relies on the spectral representation of the elastodynamic solutions for the substrate and the finite element model for the thin film. A cohesive model is introduced along the interface of the bimaterial system to capture the decohesion process. The important role of the film inertia on the crack extension and the appearance of the mixed-mode failure are demonstrated by observing the traction stress evolution at various points along the bond line. Parametric studies on the effect of film thickness, interface fracture toughness, loading pulse shape and amplitude on the debonding process are performed. A semi-analytical investigation on the inertial effect is carried out to predict the final crack length as a function of the film thickness and pulse amplitude.     

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.     

Calculations of Buckle-Driven Delamination Using Cohesive Elements

Plane strain, elastic calculations of buckle-driven thin film delamination from compliant substrates using finite element models are considered. The interfacial properties between the film and the substrate are modeled using cohesive elements with a tractionseparation law formulated in terms of a potential. The model yielded the geometry of the buckles given the properties of the film and the substrate, the interfacial toughness and the value of the compressive equi-biaxial stress. Results for the relation between the buckle width and the interfacial toughness were very close to similar results by Yu and Hutchinson (2002), thus giving confidence that the cohesive element approach presented can be used in applications where buckle-driven delamination of thin films is an issue.     

A numerical analysis of flexure induced cylindrical cracks during indentation of thin hard films on soft substrates

In this paper, the fracture behavior of a thin hard film, perfectly bonded to a soft substrate, containing circumferential (cylindrical) cracks subjected to spherical indentation is studied using the finite element method. These cracks emanate upwards from the film-substrate interface and are driven by the flexure of the film over the soft substrate under indentation. The film is taken to be linear elastic while the substrate obeys an elastic-plastic constitutive model with linear strain hardening. Three values for the substrate yield strength are considered in the analysis. The variation of energy release rate and mode mixity are examined as functions of crack length and load, for cracks located near and away from the indentation axis. The results show that, when the crack length is small, predominantly mode I conditions prevail due to tensile radial stresses near the interface. As the crack length increases, the mode mixity gradually changes from mode I to II. For cracks located near the axis, the crack growth process is stable over a range of crack lengths up to about a third of the film thickness and thereafter becomes unstable. The role of the substrate yield strength on the above issues is investigated.     

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.     

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.     

A novel boundary-domain element method of initial stress, finite deformation and discrete cracks in multilayered anisotropic elastic solids

We introduce a novel boundary-domain element method of initial stress, finite deformation (due to large rotation) and discrete cracks in multilayered anisotropic elastic solids. Because the special Green’s function that satisfies the interfacial continuity and surface boundary conditions is employed, the numerical discretization is reduced to be along one side of the cracks and over the subdomains of finite deformation. Two examples are presented. First, the process of interfacial delamination is simulated around a growing through-thickness crack in a pre-stretched film bonded to a flexible substrate. It is shown that the progression of delamination damage is stable but the initiation of delamination crack can be a snap-back instability. This simultaneous damage and fracture process is approached by the cohesive zone model. Second, the postbuckling of a circular delaminated and pre-compressed film is simulated on a flexible substrate. It is shown that the compliance of substrate can play a significant role on the critical behavior of buckling. If the substrate is more compliant or stiffer than the film, the instability initiates as a subcritical hard or a supercritical soft bifurcation. The critical magnitude of pre-strain for the initiation of buckling increases with substrate stiffness. Also, the transition of buckling from the first to the second mode is captured in the simulation.     

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.     

Hydrogen effect on fracture toughness of thin film/substrate interfaces

The effect of hydrogen on the interface fracture toughness of two nano-film/substrate structures, Ni/Si and Cu/Si, were evaluated using four-point bend specimens with and without hydrogen charging. Hydrogen typically decreases the fracture toughness of materials. However, we found in this study that the interfacial toughness between the Ni film and the Si substrate increased due to the presence of hydrogen, while that of Cu/Si decreased. Nanoindentation experiments for the Ni and Cu films revealed that local plasticity in the Ni and Cu films is promoted by the charged hydrogen. The critical stress intensity at the Ni/Si interface crack considering the plasticity of Ni, namely the true fracture toughness, is scarcely influenced by the existence of hydrogen. The apparent increase in fracture toughness of the Ni/Si interface is due to the large stress relaxation near the crack tip caused by softening due to the presence of hydrogen. Although the promotion of plastic deformation of Cu relaxes the stress intensity at the Cu/Si interface crack, the apparent interfacial toughness still decreases because of the significant decrease in the true toughness due to the presence of hydrogen.     

A review of theoretical analysis techniques for cracking and corrosive degradation of film-substrate systems

This paper contains a review of the most vital concepts regarding the analysis and design of film systems. Various techniques have been presented to analyse and predict the failure of films for all common types of failure: fracture, delamination, general yield, cathodic blistering, erosive and corrosive wear in both organic and inorganic films. Interfacial fracture or delamination is the loss of bonding strength of film from substrate, and is normally analysed based on the fracture mechanics concepts of bi-material systems. Therefore, keeping the focus of this review on bonding strength, the emphasis will be on the interfacial cracking of films and the corresponding stresses responsible for driving the delamination process. The bi-material characteristics of film systems make the nature of interfacial cracks as mixed mode, with cracks exhibiting various complex patterns such as telephone cord blisters. Such interfacial fracture phenomenon has been widely studied by using fracture mechanics based applicable analysis to model and predict the fracture strength of interface in film systems. The incorporation of interfacial fracture mechanics concepts with the thermodynamics/diffusion concepts further leads to the development of corrosive degradation theories of film systems such as cathodic blistering. This review presents suggestions for improvements in existing analysis techniques to overcome some of limitations in film failure modelling. This comprehensive review will help researchers, scientists, and academics to understand, develop and improve the existing models and methods of film-substrate systems.     

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.