We present a finite element method study of the morphology of telephone cord buckles in compressed thin films with a thickness gradient oriented perpendicular to the main buckle axis. Despite extensive studies on buckling in thin films, the influence of a transverse thickness gradient across the width of a confined telephone cord buckle remains unexplored. The analysis focuses on two morphological parameters defined as edge to peak distances asymmetry and height asymmetry evaluated over a wide range of internal stresses and thickness ratios within a confined stripe width. The results show that both in-plane and out-of-plane asymmetries exhibit only a weak dependence on internal stress and stripe width, while being strongly influenced by the thickness gradient. Increasing the gradient intensity leads to a skewing of the buckle profile toward the thinner region, consistent with the decrease of the local bending stiffness. These findings offer a new predictive scaling law for in-plane and out-of-plane asymmetry in TCBs of delaminated thin films with non-uniform thickness.

Circular buckles are known to develop morphological instabilities while expanding, above a critical diameter, as predicted in the framework of the elasticity theory. Those initial instabilities further lead to branching, then to full delamination of the films. Well-defined circular buckles are however frequently observed experimentally at large scale on ductile films. In this context, we performed finite element simulations to investigate the role of plasticity in buckles growth. Our results show that plastic deformation significantly stabilizes circular buckles by altering mode-mix and thereby enhancing interfacial toughness. These findings clarify why circular buckles persist in ductile films and highlight the implications for adhesion and durability in coated systems.

We present a novel approach for evaluating interfacial toughness in thin film-substrate systems by analyzing the propagation of straight-sided buckles in films with a well-controlled thickness gradient. Experimentally, buckles initiate in thicker regions under compressive stress and arrest consistently as the thickness decreases, where the available elastic energy is no longer sufficient to drive further delamination. This arrest mechanism is reproduced through finite element simulations incorporating a cohesive zone model. Analysis of the mode-mixity angle indicates predominantly mode-I fracture at the buckle front and mode-II fracture at the lateral edges, promoting buckle propagation toward thinner regions of the gradient. Finally, we show that the film-substrate interfacial toughness can be quantified numerically by using the critical arrest thickness of the buckle as an energetic criterion.

We investigate the mechanical and electrical properties of cuprous oxide (Cu2O) thin films processed by low-temperature oxidation of bulk annealed copper. These oxide layers were characterized using advanced techniques unveiling a microstructure composed of nanocrystalline grains. Mechanical and electrical properties were assessed through the combination of electrical-nanoindentation experiments and multiphysics numerical simulation by the Finite Element Method. Regarding the mechanical aspect, the oxide film elastic modulus was determined at 22 ± 5 GPa and its plastic behavior was successfully modeled with a Drucker-Prager yield criterion. In addition, the oxide layer was found to act as a non-penetrable barrier against dislocation gliding in the copper substrate near-surface, significantly enhancing size effects. Regarding the electrical aspect, Poole–Frenkel conduction was identified as the driving conduction mechanism in Cu2O, with a dielectric permittivity of 7 and a trap level of 320 meV, the latter result suggesting an electrical transport through hole-trapping copper vacancies.

We investigated the formation of telephone-cord buckling patterns in stressed nickel thin films deposited by ion beam sputtering on polycarbonate substrates with a controlled thickness gradient. Initially, the application of an external compressive stress induced straight-sided buckles in the nickel films. Upon releasing the applied stress, these buckles transformed into telephone-cord patterns oriented parallel to the thickness gradient, exhibiting stripe widths that varied accordingly. Experimental observations revealed that both the wavelength and width of the telephone-cord buckles decreased with decreasing film thickness. To further understand this behavior, finite element method simulations were performed to systematically study the effects of film thickness, stripe-width gradients and internal stress on the buckle wavelength. The numerical results are presented and compared with experimental data, showing good agreement and providing deeper insight into the mechanics of gradient-induced buckling in thin films.

We investigated straight-sided and telephone cord buckles on stressed nickel thin films deposited by ion beam sputtering on polycarbonate substrate and exhibiting a controlled thickness gradient. It is experimentally observed that the height of the straight-sided buckles aligned parallel to the thickness gradient decreases as the film thickness increases. When these buckles are oriented perpendicular to the gradient, they result in an asymmetrical profile with a maximum deflection shifted towards the thinner part of the film. Additionally, we explore the characteristics of telephone cord buckles, showing that their wavelength decreases as the local film thickness decreases. Finite elements method simulations were performed to systematically explore the influence of various thickness gradients on buckles. The numerical results are presented, compared to the experimental results and discussed.

We conduct a thorough investigation of the lateral growth and kinetic evolution of telephone cord buckles within thin films, employing both experimental and numerical techniques. Our exploration begins with in-situ experiments conducted on annealed silicon nitride films, aimed at capturing empirical data on the formation and evolution of these distinctive patterns. These experiments yield valuable insights into the morphological changes of telephone cords, such as wave flipping and merging, which lead to the enlargement of buckles at double wavelengths and widths. Subsequently, we employ a combined approach of geometrically nonlinear plate modeling and surface-based cohesive interface framework within a finite element numerical model to analyze the interplay between buckling-induced delamination and growth triggered by mode mixity-dependent interfacial toughness. Through this integrated approach, we effectively capture the mutual evolution of buckling and delamination occurrences, thus highlighting their inherently dynamic nature. Our numerical simulations show that the width and wavelength of telephone cords are doubled, consistent with experimental findings.

The mechanical properties of materials at the nanoscale are still poorly understood, despite intensive research efforts, in particular because mechanical tests are blind to the detailed microstructure of the samples. The latter is however crucial at small scales, when stochastic response dominates the initial elasto-plastic transition. To extract a comprehensive mechanical behavior at this scale, and despite this stochastic aspect, studying a large population of nano-objects is necessary. Additionally, investigating the early stage of the plasticity, correlated with the initial microstructure of the nano-objects, is essential. In this regard, we use a statistical approach to extract deterministic laws from various techniques such as nano-compression or nanoindentation, and we discuss the results in light with Bragg coherent diffraction imaging (BCDI) which provides the detailed crystalline state of the sample before and after mechanical testing. This ex situ approach is able to provide a more complete description of plastic behavior at small and large strains.

Thin films and coatings are used in a wide range of technological applications, such as microelectronics, packaging or optics. They often develop high residual stresses during the deposition process, sometimes about few GPa in compression. Such large compressive stresses may cause the nucleation and growth of buckling structures that generally result in the loss of functional properties that were initially conferred to such film/substrate composites. The aim of our studies is consequently to have a better understanding of the buckling phenomenon, by identifying the relevant parameters to prevent, to limit, or to control its occurrence.

Nanoindentation has now become the key technique for measuring the mechanical properties of materials at small scales. However, the quantitative and accurate processing of nanoindentation data relies on a physical quantity that is not directly available: the contact area (Ac) between the indenter tip and the sample under test. In complex systems, determining Ac is challenging due to the limitations of standard methods: analytical models have restricted validity domains (sample homogeneity and rheology), and post-mortem observations of residual imprints are time-consuming, do not appraise property gradients and cannot be applied to materials with significant elastic recovery. In this paper, a comprehensive methodology is proposed to continuously measure contact area during indentation. The proposed methodology, referred to as electrical-nanoindentation (ENI), is based on real-time monitoring of the electrical contact resistance (ECR). The protocol only requires mechanical and electrical calibrations of the indenter tip on reference materials, leading to one-to-one relationship between ECR and contact area. An original approach is also proposed to deal with the presence of surface passivating layers that generally disturb ECR measurements. As an illustration, the methodology is applied to the characterization of a multiphase alloy (MPA) composed of silver, copper and palladium. This alloy raises the same challenges as those usually faced by nanoindentation in advanced metallurgy: heterogenous distribution of individual phases at the micro-scale, composite response of a complex mixture of hard/stiff and ductile/soft phases, ... In addition, the ohmicity of contact is disturbed by surface passivating layers. Despite these numerous hindrances, the proposed methodology is successfully applied to this material. The evolution of contact area is compared with standard methods: an impressive accuracy of <2% standard-deviation is achieved when compared to post-mortem observations. The elastic moduli and hardnesses of individual phases are then accurately extracted. In addition, in order to gain in spatial definition, the ENI set-up is integrated into a scanning electron microscope (SEM), enabling indent positioning with a precision close to 100 nm. Two challenges are successfully met with the ENI methodology. On a mechanical point of view, the response of individual phases can be identified despite the complex rheology of heterogeneous materials, proving the approach applies to all mechanical behaviors (sink-in or pile-up rheologies, homogeneous or heterogeneous materials, with or without elastic recovery, ...). On an electrical point of view, even if contact ohmicity is the only requirement of the methodology, it is possible to identify and overcome deviations from contact ohmicity induced by surface passivation. In particular, the non-linear resistive contribution of insulating layers fades during indentation thanks to its dependence as the reciprocal of the square of contact radius. The present work provides the keys to monitoring the contact area on any metallic sample, whether oxide-free or oxidized, making this methodology a promising alternative to standard methods.

We report on circular buckles experimentally observed by optical and atomic force microscopy on gold ductile thin films deposited by physical vapor deposition on silicon wafers. It is shown that, whatever the radius blister dimensions, their maximum deflections are higher than those expected by the elastic theory. It suggests that plastic events may take place in the film, impacting on the blister morphology as a result. Based on nanoindentation experiments carried out on our gold films, a proper plastic hardening law has been determined by calculations using the finite elements method. The influence of this elasto-plastic behavior on the buckled circular profiles has been then numerically studied, compared to the experimental observations and discussed.

We report on straight-sided buckles experimentally observed by optical and atomic force microscopies on gold ductile thin films deposited by physical vapor deposition on silicon wafers. It is shown that, whatever the buckle dimensions, their maximum deflections are higher than those expected by the elastic theory. Finite elements simulations taking into account plastic deformations in the film have been carried out. The numerical results are presented, discussed and compared to the experimental observations.

Single-crystal and fine-grained polycrystalline samples of Cr2AlC were oxidized under dry air flow at temperature in the 1000-1400 degrees C range during 100 h. A continuous alumina layer forms on top of the Cr2AlC surface whereas a Cr7C3 sublayer also appears. In-lab characterization of oxidized Cr2AlC samples shows strong damaging at the free surface, resulting from the buckling of the alumina scale. In-situ X-ray diffraction measurements under synchrotron radiations were performed to measure the lattice strain during the first hours of oxidation process and further calculate the internal stress in the Al2O3 layers. Alumina layers undergo tensile stress during isothermal oxidation, showing that the buckling of the alumina scale does not result from the oxide growth. Such a tensile stress likely results from the Cr2AlC to Cr7C3 phase transformation. During cooling, the tensile stress decreases down to compressive values, due to the thermal expansion coefficient mismatch between the film and the substrate, leading to buckling of the alumina layer. It is demonstrated that the dimensions of the buckles cannot be explained either by gas pressure or by the magnitude of the internal compressive stress in the alumina scale after cooling. The discrepancy between the experimental maximum deflection and the one predicted by the elastic theory can only be explained by a significant plastic deformation occurring in the alumina scale.

DCB and Wedge tests are widely used in experimental fracture mechanics in order to identify fracture properties of materials or assembled parts, like toughness. In order to extract data from those experiments, it is very common to model the sample as two adhesive beams with a crack growing in between as an external loading is applied. This study is devoted to investigating the influence of two types of beam kinematics on the identification of the cohesive zone parameters of interfaces. A critical comparison between beam models based on an Euler–Bernoulli or a Timoshenko beam kinematics is carried out in the case of the DCB and Wedge loaded DCB tests. The size of the process zone extent is used as a parameter to evaluate the difference between the two models predictions. Euler–Bernoulli kinematics neglects the effect of shear stress on the beam's deflection whereas Timoshenko kinematics accounts for it. The aim of the present work is to evaluate the validity of each kinematics, both used in the literature, especially when the process zone length becomes comparable to the specimen's height. In both frameworks, an analytical prediction is presented and compared over a wide range of cohesive zone parameters and beam geometries, using a non-dimensional representation. Our results show that when we compare both kinematics in term of the fracture process zone, the relative error varies from a few percent to more than 1000%, depending on the specimen's geometry, properties and the loading conditions. In addition, for many cases, no Euler–Bernoulli kinematics can fit the Timoshenko kinematics, especially around the fracture process zone. The cases for which Timoshenko and Euler–Bernoulli kinematics yield similar results are highlighted. The model and the results of the study can be used as a guideline for users in order to determine which model is required in order to get an accurate determination of the cohesive parameters in their particular system of interest.

Functional devices such as microelectronic systems, solar cells and power devices are composed of complex stacks of various materials, including semiconductors, ceramics and metallic alloys. The knowledge of the mechanical response of those stacks is a key point, as they are submitted to harsh stresses during the fabrication process (induced by thermal treatments, mechanical polishing, packaging processes, ...) as well as during the device lifetime.& nbsp;We report the mechanical study of a microelectronic-dedicated stack where a silicon nitride (Si3N4) layer was deposited on top of a thick metallic alloy (AlSiCu) layer. In microelectronic chips, Si3N4 is widely used as a passivation layer, while AlSiCu is the electrical connection layer. The structure has been tested experimentally by nanoindentation. Multiple pop-in events were observed on the loading curves, indicating multiple cracking, with cracks initiated at various loading stages. The high reproducibility of the loading curves then allowed their full analysis by numerical modeling.& nbsp;The complete damage process of the multilayer during indentation is analyzed using modeling by the Finite Element Method (FEM), accounting for plasticity in AlSiCu, crack propagation in the Si3N4 layer and possible delamination at the interface between the two layers. The various stages of the damage process occurring in the Si3N4 are elucidated, showing in particular the occurrence of a first crack in the region underneath the indenter (hence not visible by a surface observation), followed by a second crack forming further away from the indenter, on the top surface of the layer. Moreover, a novel procedure for the identification of the Si3N4 layer tensile strength is presented, using an inverse method based on FEM simulations and experimental data. The results of the simulations (cracking patterns and cracks locations) are also further validated by the observation of structure cross-sections with a Scanning Electron Microscope (SEM) after Focused Ion Beam (FIB) milling of the sample. In addition, the proposed identification procedure is quite generic and can be adapted to other systems showing similar multiple-cracking patterns under indentation.

Advanced devices (for microelectronics, energy storage, power sourcing) are complex architectures of metals and dielectrics subjected to harsh mechanical stresses. The functional reliability of the embedded dielectrics is driven by their ability to preserve their electrical properties (such as leakage and breakdown). Accordingly, understanding the interplay between the mechanical and electrical behaviors of dielectric films is critical to predict the lifetime of functional devices. In this study, the effect of plastic deformation on the electrical conduction of an ultra‐low‐k dielectric film is elucidated by combining in situ advanced experiments and finite element modeling. Experimentally, “electrical‐nanoindentation” tests emphasize the strong correlation between electrical and mechanical failures (leakage degradation, breakdown, plasticity, cracking). These experiments also reveal a counterintuitive electrical conduction drop under high mechanical stresses. This phenomenon is reproduced numerically by correcting the Poole–Frenkel conduction law with a strain‐dependent factor, and described analytically in terms of space‐charge build‐up induced by the trapping of holes at the mechanically generated defects. A threshold strain is identified as the keystone relating this strain‐dependent conduction to the current line distribution within the dielectric. This study provides a new understanding of the mechanical/electrical couplings in dielectrics, which opens promising insights into reliability issues for advanced devices.

This paper reports the experimental, analytical, and numerical study of resistive-nanoindentation tests performed on gold samples (bulk and thin film). First, the relevant contributions to electrical contact resistance are discussed and analytically described. A brief comparison of tests performed on gold and on natively oxidized metals highlights the high reproducibility and the voltage-independence of experiments on gold (thanks to its oxide-free surface). Then, the evolution of contact resistance during nanoindentation is fully explained in terms of electronic transport regimes: starting from tunneling, electronic transport is then driven by ballistic conduction before ending with pure diffusive conduction. The corresponding analytical expressions, as well as their validity domains, are determined and compared with experimental data, showing excellent agreement. From there, focus is made on the diffusive regime. Resistive-nanoindentation outputs are fully described by analytical and finite-element modeling. The developed numerical framework allows a better understanding of the main parameters: it first assesses the technique capabilities (validity domains, sensitivity to tip defect, sensitivity to rheology, effect of an oxide layer, and so on), but it also validates the different assumptions made on current line distribution. Finally, it is shown that a simple calibration procedure allows a well-resolved monitoring of the contact area during resistive-nanoindentation performed on samples with complex rheologies (ductile thin film on an elastic substrate). Comparison to analytical and numerical approaches highlights the strength of resistive-nanoindentation for continuous area monitoring.

The rising complexity of multi-material structures integrated into multi-functional devices requires the development of dedicated characterization tools capable of simultaneously monitoring different physical magnitudes with a relevant spatial resolution. This paper reports the development and the application of an original instrument based on a nanoindenter coupled with fine electrical measurements and integrated in-situ a Scanning Electron Microscope (SEM). The performances and capabilities of this home-developed instrument are illustrated through two different case studies. First, a micrometer-scale piezoelectric structure made up of wurtzite-single crystalline AlN islands grown on top of conductive Si pillars is tested. In-situ SEM imaging is used to precisely position the indenting probe on these individual islands, while the instrument sensitivity and repeatability are used to monitor their low-signal piezoresponse. Effective piezoelectric coefficients are also extracted for different loading/unloading conditions. Secondly a Si3N4/AlSiCu/SiO2 stack, which is standardly integrated as a passivation structure on top of microelectronic chips, is electrically and mechanically stressed and monitored up to its failure. The mechanical failure mechanisms (buried or emerging cracks) are discriminated thanks to the real-time SEM imaging of the indentation test. The instrument high sensitivity is used to monitor early current leakages that are attributed to conduction paths induced by mechanical failures. Combining high electro-mechanical sensitivity and precise probe positioning appears as an efficient way to monitor and analyze low-level electrical responses of small-scale structures. This approach paves the way to the fine characterization of micro/nano-systems displaying mechanically-driven electrical properties (conduction mechanism, leakage, breakdown,) like 2D-materials, dielectrics in microelectronic devices, strain-sensors, enamelled Litz wires,...

Thin films submitted to internal/external stresses are known to undergo buckling over a critical stress level. In the case of a rigid substrate, depending on the stress anisotropy, three elementary buckling structures are expected: straight-sided, bubble or telephone cord buckles. In this context, the effect of the substrate elasticity on the expected buckled morphologies is explored. The post-buckling equilibrium shapes that develop on parallel delaminated stripes of films for a biaxial compressive stress state are studied. Finite elements methods calculations are carried out to simulate the various equilibrium configurations. A morphological map is extracted and plotted as a function of the stress components in the longitudinal (i.e. along the stripe direction) and transversal direction (i.e. perpendicular to the stripe direction). It is shown that the stability domains of the elementary buckles are shifted down to lower stresses as the substrate stiffness is decreased. In addition, the stability domain of the telephone cord buckles is shown to be enlarged. Finally, an intermediate domain between bubbles and both straight-sided and telephone cord buckles is evidenced on the morphological map. The buckles are in this case characterized by hook-like or bone-like structures. This latter buckling structure has been experimentally observed by atomic force microscopy on nickel/polycarbonate systems.

We report on buckling structures observed on tantalum films deposited by sputtering on silicon wafers. It is shown that, above a critical diameter, the circular blisters evolve to ring-shaped buckles, whatever the smooth or undulating type of their edges. The experimental results have been compared to finite element simulations. In particular, the polygonal collapsed part at the center of the buckles can be well understood by taking into account the pressure mismatch between the inside and outside parts of the buckles.