Ductility Of Thin Films Research Articles

Influence of elasto-plastic behavior of thin films on circular buckling structures

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.

Elastic-plastic buckling of gold thin films into straight-sided blisters

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.

Adhesion strength of ductile thin film determined by cross-sectional nanoindentation

Cross-sectional nanoindentation (CSN) is a powerful tool for measuring the adhesion strength of thin films. However, a quantitative assessment of interfacial properties for metal thin films on brittle substrates remains a challenge due to thin film ductility. In this work, we present a hierarchical analysis method to account for plastic dissipation during delamination. According to our observations, the CSN-induced wedge geometry is more complex than what is currently presented in literature. Therefore, we develop a three-dimensional finite element (FE) modelling strategy to simulate CSN-induced delamination. Furthermore, we present the mode mixity distribution during CSN measurement based on our simulation results. We find that a purely experimental assessment of adhesion strength by CSN for ductile thin films is imprecise due to the adhesion strength-dependent stress-state in this characterization technique. By using our combined experimental and numerical approach, the adhesion strength of EBPVD-deposited Al thin film on SiO2/Si substrate is determined as 0.577 J/m2 and an additional 20 nm thick Ti adhesion layer enhances its adhesion strength to 16.4 J/m2.

Buckling and folding of a ductile thin film on a rigid substrate

The buckling of a thin film deposited on an infinitely rigid substrate and delaminated over a finite length is studied in the framework of the Föppl-von Kàrmàn theory of thin plates. Assuming the two edges of the ductile film can fold, an energy-based analysis of the different morphologies of the film has been carried out. Depending on the delamination length, the film can either be unfolded, partially folded at one edge or symmetrically folded at its two edges.

Influence of Side Chain Interdigitation on Strain and Charge Mobility of Planar Indacenodithiophene Copolymers.

Indacenodithiophene (IDT) copolymers are a class of conjugated polymers that have limited long-range order and high hole mobilities, which makes them promising candidates for use in deformable electronic devices. Key to their high hole mobilities is the coplanar monomer repeat units within the backbone. Poly(indacenodithiophene-benzothiadiazole) (PIDTC16-BT) and poly(indacenodithiophene-thiapyrollodione) (PIDTC16-TPDC1) are two IDT copolymers with planar backbones, but they are brittle at low molecular weight and have unsuitably high elastic moduli. Substitution of the hexadecane (C16) side chains of the IDT monomer with isocane (C20) side chains was performed to generate a new BT-containing IDT copolymer: PIDTC20-BT. Substitution of the methyl (C1) side chain on the TPD monomer for an octyl (C8) and 6-ethylundecane (C13B) afford two new TPD-containing IDT copolymers named PIDTC16-TPDC8 and PIDTC16-TPDC13B, respectively. Both PIDTC16-TPDC8 and PIDTC16-TPDC13B are relatively well deformable, have a low yield strain, and display significantly reduced elastic moduli. These mechanical properties manifest themselves because the lengthened side chains extending from the TPD-monomer inhibit precise intermolecular ordering. In PIDTC16-BT, PIDTC20-BT and PIDTC16-TPDC1 side chain ordering can occur because the side chains are only present on the IDT subunit, but this results in brittle thin films. In contrast, PIDTC16-TPDC8 and PIDTC16-TPDC13B have disordered side chains, which seems to lead to low hole mobilities. These results suggest that disrupting the interdigitation in IDT copolymers through comonomer side chain extension leads to more ductile thin films with lower elastic moduli, but decreased hole mobility because of altered local order in the respective thin films. Our work, thus, highlights the trade-off between molecular packing structure for deformable electronic materials and provides guidance for designing new conjugated polymers for stretchable electronics.

Non-isocyanate Polyurethanes from 1,1'-Carbonyldiimidazole: A Polycondensation Approach.

1,1'-Carbonyldiimidazole (CDI) provides a platform to generate high molecular weight polyurethanes from industrially relevant diols and diamines. CDI, which is described in the literature for its use in amidation and functionalization reactions, enables the production of well-defined and stable polyurethane precursors, thus eliminating the need for isocyanates. Herein, the functionalization of 1,4-butanediol with CDI yields an electrophilic biscarbamate, bis-carbonylimidazolide (BCI), which is suitable for further step-growth polymerization in the presence of amines. Elevated reaction temperatures enable the solvent-, catalyst-, and isocyanate-free polycondensation reaction between the BCI monomer and various diamines. The thermoplastic polyurethanes produced from this reaction demonstrate high thermal stability, tunable glass transition temperatures based on incorporation of flexible polyether segments, and mechanically ductile thin films. CDI functionalized diols will allow the preparation of diverse polyurethanes without the use of isocyanate-containing monomers.

Numerical simulation of peel test for ductile thin film along ceramic substrate: Elasto-plastic analysis

Due to extensive applications of the thin film/substrate systems in engineering, the research on strength, ductility and reliability of these systems have attracted great deal of interest in recent years. The peel angle of debonded film on the ceramic substrate has a very important effect in the mechanical resistance of film/substrate bi-material. Among critical debonding parameters, peeling angle and thermal residual stresses can be a potential risk of brutal propagation causing the film/substrate composite failure under tensile loading. This study is carried out to analyze the peeling angle and residual thermal stresses effects with crack growth in the specimen. A two dimensional elastic-plastic finite element model is used to compute the J-integral and estimate the plastic zone size at the interfacial crack tip of film/substrate composite. Results show that the peeling phenomena is a fracture mixed mode where the dominance of either mode I or mode II is influenced by the peeling angle while delamination of thin film is greatly dependent on thermal residual stresses.

Resistive-nanoindentation on gold: Experiments and modeling of the electrical contact resistance.

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.

Elastic–plastic analysis of the peel test for ductile thin film presenting a saturation of the yield stress

The paper investigates the peel test of an elastic–plastic film on an elastic substrate. The case of a film material presenting a saturation of the yield stress is considered. Based on earlier approaches of the literature, see for instance Kim and Aravas (Int J Solids Struct 24:417–435, 1988), a semi-analytical expression for the work done by bending plasticity is proposed. The validity of the present expression is established based on finite element calculations. It is shown that for the interpretation of the results of peel test at 90$$^{\circ }$$ when the peel force and the curvature are measured, the present approach can provide a precise value of the interface fracture energy.

Interface toughening in multilayered systems through compliant dissipative interlayers

The effect on an interlayer on the toughness of an interface between a ductile thin film and an elastic substrate is investigated by finite element modeling and assessed towards experimental measurements. The model is based on an asymptotic K-field formulation relying on cohesive zone elements to simulate the fracture process. A compliant interlayer tends to increase the interface toughness by promoting plastic dissipation in the thin layer. Additional toughening can result from the development of plastic strains in the interlayer. The magnitude of these two toughening mechanisms depends on the film thickness, among other parameters. The model predictions are confirmed by comparison with wedge-opening test data performed on a multilayer composed of a thin Cu layer and a polymer interlayer embedded between two stainless steel substrates. These findings lay the foundation for the design of tougher multilayers and provide a critical assessment of experimental protocols for interface toughness measurements requiring the bonding of a dummy substrate, such as used for DCB or four point bending tests.

Quantifying the Fracture Behavior of Brittle and Ductile Thin Films of Semiconducting Polymers

One of the primary complications in characterizing the mechanical properties of thin films of semiconducting polymers for flexible electronics is the diverse range of fracture behavior that these materials exhibit. Although the mechanisms of fracture are well understood for brittle polymers, they are underexplored for ductile polymers. Experimentally, fracture can be characterized by observing the propagation of cracks and voids in an elongated film. For brittle polymers, we find that films bifurcate in such a way that the crack density increases linearly with applied strain (R2 ≥ 0.91) at small strains. Linear regression is used to estimate the fracture strength and strain at fracture of each material using an existing methodology. For the case of ductile polymers, however, we find that diamond-shaped microvoids, which originate at pinholes and defects within the film, propagate with an aspect ratio that increases linearly with applied strain (R2 ≥ 0.98). We define the rate of change of the aspect ratio ...

Fragmentation testing for ductile thin films on polymer substrates

Fragmentation testing of thin films on substrates has in the past been mostly performed in situ using optical and scanning electron microscopy. While these techniques work well for brittle materials, they cannot always discern the difference between through-thickness cracks (TTCs) and localized plastic deformation of ductile films. Here, we describe fragmentation testing with atomic force microscopy and present criterion to distinguish TTCs and localized deformation for ductile films.

Characterization of the adhesion of thin film by Cross-Sectional Nanoindentation: Analysis of the substrate edge chipping and the film delamination

Cross-Sectional Nanoindentation (CSN) is a recent method for adhesion measurement of nanoscale thin films in Ultra-Large Scale Integrated circuits. In the case of ductile thin films, the motion of the substrate chip implies significant plastic deformation of the film and complex geometry of delaminated areas. This article recalls first the experimental procedure and the two main features observed in this test performed on various plane copper films deposited on silicon: the critical force producing silicon edge chipping increases linearly with the distance of the indenter to the interface; on the section the delaminated length of the film ( a − b ) is proportional to the residual silicon chip displacement u f and the ratio S = u f / ( a − b ) depends on the manufacturing process of the film, and is so related to its adhesion to the substrate. One proposes a simple analysis of the silicon edge chipping. Then a model of pull-off of an elastic-strain hardening plastic film is developed, which suggests an explanation for the delamination process. Application of the model to experimental results starting from films plastic properties deduced from nanoindentation measurements provides plausible results. Some improvements for performing the CSN test are proposed in order to make easier its interpretation.

Channel cracking in inelastic film/substrate systems

Studies on channel cracking are generally limited to elastic films on elastic or inelastic substrates. There are important applications were the cracking process involves extensive plasticity in both the film and substrate, however. In this work steady-state channel cracking in inelastic thin-film bilayers undergoing large-scale yielding from thermal or mechanical loading is studied with the aid of a plane-strain FEA. The plasticity of the film and substrate, represented by a Ramberg–Osgood constitutive law, each increases the energy release rate (ERR) relative to the linearly-elastic case. This effect is more pronounced under mechanical loading where the entire bilayer undergoes large-scale yielding. To help assess the analytic approach some fragmentation tests are performed using a well-bonding epoxy/aluminum system. The analysis reproduced well the observed dependence of crack initiation strain on film thickness. Ultra-thin films may be well represented by an elastic-perfectly plastic response. For such films on a flexible support the ERR remains fixed as the applied strain exceeds the yield strain of the film. Accordingly, a critical coating thickness exists below which no channel cracking is possible. The explicit relations and graphical data presented may be used for optimal design of such structures against premature failure as well as for determining fracture energy of ductile thin films.

Microstructure–property relationship in highly ductile Au–Cu thin films for flexible electronics

The new and fast emerging field of flexible electronic devices requires highly ductile materials. Deposition of thin metal films on flexible substrates is a suitable method to create highly ductile interconnects. In this study, thin films consisting of a graded composition of Au–Cu were co-deposited by direct-current magnetron sputtering on polyimide (Kapton ®) substrate for in situ SEM tensile testing, while silicon wafer supported thin film spreads were characterized by nanoindentation, XRD and EDX. Substrate quality turned out to be extremely important for strain delocalization to allow for uniform deformation characterized by high ductility. No cracking was observed up to the maximal strain of 30% for films consisting of pure gold and alloys with a low copper content up to 10 at.%, while cracking was more prevalent in films with higher copper contents and with applied heat treatment. In the most ductile thin films shear bands are the precursors of ductile cracks.

MEMS-based microstructures for nanomechanical characterization of thin films

The measurement of mechanical properties of thin films is a major issue for the designof reliable microelectronic devices, microsensors or thin coatings. New simplemicrostructures actuated through the release of internally stressed long beamsmade of high temperature, low pressure chemical vapour deposition silicon nitridehave been developed to test under uniaxial tension submicron thin film materialspecimens. The relative displacement between a fixed and a moving cursor is used todetermine the strain applied to the specimen. The stress is inferred based onthe mismatch strain and Young’s modulus of the silicon nitride actuator beam.By multiplying the tensile test microstructures with different lengths, the fullstress–strain curve characterizing the thin material sample is generated fromwhich the elastic stiffness, yield strength, ductility and fracture stress can beextracted. The potential of the method is demonstrated through applicationson both brittle and ductile thin films. The Young’s modulus of 238 GPa for a373 nm thick silicon nitride film is extracted and size effects are observed for theyield strength of pure aluminium with a value of 220 and 550 MPa, respectively,for 373 and 205 nm thick films. An original variant of the procedure based onthis new test microstructure for measuring Young’s modulus is also presented.

A three-dimensional finite element analysis of interface delamination in a ductile film/hard substrate system induced by wedge indentation

Interface delamination and arching of a ductile thin film on a hard substrate subject to microwedge indentation were investigated systematically using a three-dimensional finite element method. A traction–separation law was introduced to simulate the cohesion and failure behavior of the interface between the film and the substrate. The effects of the interface strength and the length of the microwedge indenter on the onset and growth of interface delamination and film arching were analyzed. It was shown that a two-dimensional to three-dimensional transition of stress state occurs during indentation, depending on the indenter length and indentation depth. Conditions for using two-dimensional and three-dimensional models were suggested.

Development of a fatigue testing system for thin films

Only a few works on fatigue behavior of thin films under tension–tension loading can be found because of some limitations of a testing system. In this study, a fatigue testing system capable of performing load controlled tension–tension fatigue tests even for ductile thin films was developed by using an electrodynamic actuator. With the system, fatigue testing can be performed over a wide range of loading frequency. Besides, a capacitive displacement gauge was developed to measure the monotonic and cyclic deformation of thin films with high resolution during fatigue testing. As the displacement gauge is stable and its response is so fast, the displacement can be measured instantaneously and continuously during fatigue testing of high frequency.

Peeling experiments of ductile thin films along ceramic substrates – Critical assessment of analytical models

Two types of peeling experiments are performed in the present research. One is for the Al film/Al 2O 3 substrate system with an adhesive layer between the film and the substrate. The other one is for the Cu film/Al 2O 3 substrate system without adhesive layer between the film and the substrate, and the Cu films are electroplated onto the Al 2O 3 substrates. For the case with adhesive layer, two kinds of adhesives are selected, which are all the mixtures of epoxy and polyimide with mass ratios 1:1.5 and 1:1, respectively. The relationships between energy release rate, the film thickness and the adhesive layer thickness are measured during the steady-state peeling process. The effects of the adhesive layer on the energy release rate are analyzed. Using the experimental results, several analytical criteria for the steady-state peeling based on the bending model and on the two-dimensional finite element analysis model are critically assessed. Through assessment of analytical models, we find that the cohesive zone criterion based on the beam bend model is suitable for a weak interface strength case and it describes a macroscale fracture process zone case, while the two-dimensional finite element model is effective to both the strong interface and weak interface, and it describes a small-scale fracture process zone case.

Cross-sectional nanoindentation for copper adhesion characterization in blanket and patterned interconnect structures: experiments and three-dimensional FEM modeling

Cross-sectional nanoindentation (CSN) is a recent method for adhesion measurement of nanoscale thin films in ultra-large scale integrated circuits. In the case of ductile thin films, plastic deformation during the test and complex geometry of delaminated areas require 3D finite element modeling (FEM) for adhesion energy calculation. In this paper the adhesion of various copper (Cu) films on blanket and patterned structures is studied by CSN test. The experimental procedure and qualitative analysis of the test are presented in detail. Crack propagation is studied on blanket and patterned substrates. The dimensions of delaminated blisters are measured by scanning electron microscope (SEM) for each sample. Results show that a geometrical ratio can be used to give a quick and qualitative measurement of adhesion. A new 3D FEM model is then proposed to assess quantitative analysis of CSN test. The deformation energy of Cu blister is calculated for each sample. The mechanical properties of the Cu films required for numerical calculations are measured by instrumented indentation. The influence on these measurements of the evolution of the Cu deformation with penetration depth is discussed in detail with the aid of 2D numerical simulation. The results of numerical modeling correlate well with qualitative evaluation of adhesion.