A finite element model for the analysis of buckling driven delaminations of thin films on rigid substrates

The delamination process of thin films on rigid substrates is investigated. Such systems are typically subject to high residual compression and modest adhesion causing them to buckling driven blisters. In certain cases buckles with the shape of telephone cords are observed. A finite element model for quasi–static delamination growth is developed. Applying a Reissner–Mindlin shell kinematic for the film allows C ⁰− continuous shape functions. The traction vector at the film–substrate interface is obtained from the derivative of a cohesive free energy. Incorporation of loading and unloading conditions is considered for the irreversible process. The equilibrium state is computed iteratively in dependence of the compressive residual stresses. The computed telephone cord delaminations are stable asymmetric configurations whereas the symmetric configurations are unstable.     

Nanocrystalline silicon thin films on PEN substrates

We study the structural and electrical properties of intrinsic layer growth close to the transition between amorphous silicon (a-Si:H) and nanocrystalline silicon (nc-Si:H), deposited on glass and PEN without intentional heating. These samples showed different behaviour in Raman shift and XRD spectra when compared with that of samples deposited at 200 °C. Electrical properties of these films also reflect the transition between a-Si:H and nc-Si:H, and put in evidence some differences between the microstructure of the films grown on PEN and on glass.P- and n-doped layers were deposited onto glass substrate without intentional heating and at 100 °C with thicknesses ranging from 1000 nm to 35 nm. Conductivity measurements indicate the capability of doping this material, but, for very thin layers, substrate heating was found to be essential.     

Mechanical buckling instability of thin coatings deposited on soft polymer substrates

Deformation of rubber and poly(ethylene terephthalate) coated with a platinum or a gold film was studied. The thickness of the coating film was approximately ten nanometers. The polymer substrates were 10⁴ to 10⁵-fold softer than the coating. Folding of the coating leading to the appearance of a wave-like pattern on an originally smooth surface was observed both in tension and after shrinkage. In tension the wave crests are oriented along the elongation direction. After shrinkage the wave crests are perpendicular to the shrinkage direction. For rubber substrates, the appearance of the wave is explained by a mechanical buckling instability of the coating under compressive force. The length of the surface wave depends on the thickness of the coating layer and the rigidity of the polymer substrate. In addition to folding, regular fragmentation of the coating film on long and comparatively narrow bands is observed. The cracks are perpendicular to the wave crests both in tension and after shrinkage.     

The effect of interaction of loadings and geometry imperfection on the buckling state of frames

In this paper the effect of the interaction of two loadings, and of the deviation from right angle on the buckling mechanism of a rectangular two-bar frame is discussed. Using a nonlinear stability analysis it is found that there is a critical value of the ratio of the two loadings, as well as of the deviation from right angle, for which the physical equilibrium path and the physically unacceptable complementary path meet each other at an asymmetric bifurcation point. At this point, the response of the frame changes from an elastic limit point instability to a stable equilibrium path associated with inelastic buckling. The analysis is supplemented by a variety of numerical results obtained by an efficient and reliable simplified nonlinear stability analysis applied for the first time to a non-rectangular frame.     

Influence of substrate compliance on buckling delamination of thin films

A thin film subject to in-plane compressive stress is susceptible to buckling-driven delamination. This paper analyzes a straight-sided delamination buckle with a focus on the effects of substrate compliance, following earlier work by B. Cotterell and Z. Chen. The critical buckling condition, the energy release rate and the mode mix of the interface delamination crack are calculated as a function of the elastic mismatch between the film and substrate. The average energy release rate at the curved end of a tunneling straight-sided blister is also determined. The more compliant the substrate, the easier for the film to buckle and the higher the energy release rates. The effect becomes significant when the modulus of the substrate is appreciably less than that of the film. When the substrate modulus is comparable to that of the film, or higher, the usual assumption is justified to the effect that the film is clamped along its edges. When the substrate is very compliant the energy release rate at the curved front exceeds that along the straight sides.     

Lead zirconate titanate thin films on GaAs substrates

Thin films of the piezoceramic lead zirconate titanate (PZT) of composition Pb(Zr0.53Ti0.47)O3 have been prepared on a platinized GaAs substrate system using a propanediol based sol-gel technique. A Si3N4 buffer layer was deposited onto the GaAs by plasma-enhanced chemical vapour deposition so as to minimize Ga and As diffusion during film fabrication. Rapid thermal processing (RTP) techniques were used to thermally decompose the sol-gel layer to PZT in a further effort to avoid problems of Ga and As diffusion. Adhesion between the electrode and substrate was found to improve when an intermediate Ti layer deposited between the Pt and Si3N4 was oxidized prior to depositing the Pt layer. A crystalline PZT film was produced on the Pt/TiO2/Si3N4/GaAs by firing the sol-gel coating at 350°C for 1 min and then at 650°C for 10 s using RTP. A single deposition of precursor sol resulted in a film 0.5 μm thick. Measured average values of remanant polarization and coercive field were 14 μC cm-2 and 47 kV cm-1, respectively. The polarization value is rather low, as conventionally fired films on silicon have remanent polarization values of 20–30 μC cm-2; the lower values may be due to incomplete crystallization during RTP, but a degradation of properties due to Ga-As diffusion, despite the precautions, cannot be ruled out at this stage. This revised version was published online in November 2006 with corrections to the Cover Date.     

The effect of geometric imperfections on the buckling behaviour of composite laminated cylinders under external hydrostatic pressure

Using a new FE modelling procedure for the accurate representation of a geometrically imperfect cylinder, the present study investigates the effect of the initial imperfection magnitude on the cylinder buckling load, when it is loaded by external hydrostatic pressure. The buckling behaviour of a carbon/epoxy filament wound cylinder is initially studied and the modelling procedure is validated through a comparison between calculated and experimental results. Various FE models are developed and evaluated, with increasing degree of complexity. The method is then applied to a cylinder with different end supports, to assess how the boundary conditions together with the imperfections affect the buckling behaviour. Finally, the effect of imperfection magnitude is investigated, leading to the calculation of knockdown factors as low as 0.6.     

Ductility of thin copper films on rough polymer substrates

Electronic components in modern flexible electronics are connected by interconnects, which typically have the form of metal films resting on polymer substrates. This paper firstly studies experimentally the ductility of Cu films deposited on polyimide substrate with roughened surface (due to sandblasting) and finds that, upon tensile loading along the direction of film surface, the density of surface cracks in the film decreases with increasing surface roughness. The method of finite elements is subsequently employed to study the distribution of tensile stresses in the film and their influence on film cracking (initiation and propagation). It is demonstrated that a rough (curved) interface can reduce the tensile stresses along the film surface so as to restrain channel cracking of the film. Finally, the cohesive zone model is used to study the initiation and spreading of damage in the film and interfacial debonding of the curved interface. Both the interfacial damage and interface crack length are reduced as a result of interface roughening.     

Electrical properties of thin PbTe films on Si substrates

An attempt was made to reduce the carrier concentration in thin PbTe films on Si substrates by optimizing deposition conditions. A modified hot-wall method was used for reproducible growth ofp-type films with 5 × 10¹⁵ < p(77 K) < 5 × 10¹⁷ cm^-3 andn-type films with 3 × 10¹⁵ < n(77 K) < 5 × 10¹⁶ cm^-3. The IR irradiation was found to have a significant effect on the temperature variation of film resistance. The activation energy of the IR-sensitivity centers was determined to be 0.11 ± 0.005 eV at room temperature and 0.18 ± 0.005 eV between 150 and 180 K.     

Thermal stability of silver thin films on zirconia substrates

The thermal stability of silver thin films between 100 nm and 820 nm thick deposited onto single crystal yttria-stabilised zirconia (YSZ) substrates by evaporation was investigated by annealing the films between 250 °C and 550 °C for different durations. Films approximately 100 nm thick were thermally unstable at temperatures as low as 250 °C. A dewetting process occurred in which grain boundaries ruptured, to uncover the substrate and reduce the overall energy of the system, by a combination of grain boundary grooving at the outer surface and void growth at the Ag-YSZ interface. The surface self diffusion coefficient of Ag was determined from the kinetics of the process to be 2.6 ± 0.3 × 10^− 5 cm²s^− 1 at 500 °C. The resulting silver morphology ranged from ‘self-organised’ interconnected silver network structures to completely isolated silver islands. A structure predominance map of the rearrangement process is presented.     

Plasma oxidation of Al thin films on Si substrates

In this study, Al thin films deposited on silicon wafers by direct current magnetron sputtering were oxidized under radio frequency 13.56 MHz O₂ plasma at temperatures up to 550 °C. During oxidation, plasma powers as well as oxidation temperature and time were varied to investigate the oxidation behavior of the Al films. X-ray photoelectron spectroscopy and Auger electron spectroscopy results show that the apparent alumina could be observed after O₂ plasma treatment with powers above 200 W as well as at temperatures above 250 °C. However, no alumina increment could be discerned after individual either heat treatment at 550 °C or plasma treatment at room temperature. The thickness of alumina layers increased remarkably with plasma power and could reach about 60 nm when undergone 400 W O₂ plasma treatment at 550 °C for 2 h. Moreover, the thickness of alumina increased parabolically with time during plasma oxidation aided by thermal treatment. The deduced activation energy of such plasma oxidation was 19.1 ± 0.5 kJ/mol.     

Nanostructuring thin Au films on transparent conductive oxide substrates

Fabrication processes of Au nanostructures on indium-tin-oxide (ITO) surface by simple, versatile, and low-cost bottom-up methodologies are investigated in this work. A first methodology exploits the patterning effects induced by nanosecond laser irradiations on thin Au films deposited on ITO surface. We show that after the laser irradiations, the Au film break-up into nanoclusters whose mean size and surface density are tunable by the laser fluence. A second methodology exploits, instead, the patterning effects of standard furnace thermal processes on the Au film deposited on the ITO. We observe, in this case, a peculiar shape evolution from pre-formed nanoclusters during the Au deposition stage on the ITO, to holed nanostructures (i.e. nanorings), during the furnace annealing processes. The nanorings depth, height, width, and surface density are shown to be tunable by annealing temperature and time.     

Synthesis and characterization of vanadium oxide thin films on different substrates

In this study, the V₈O₁₅ derivative of vanadium oxide was produced on plain glass, indium tin oxide and silicon wafer substrate layers by taking advantage of wet chemical synthesis which is an easy and economical method. The structural properties of the produced films were examined by XRD and SEM analyses. Besides, Al/VO_x/p-Si metal-oxide-semiconductor (MOS) structure was obtained by the same synthesis method. Doping densities of these MOS structures were calculated from frequency dependent capacitance–voltage measurements. It was determined that the interface states which were assigned with the help of these parameters vary according to frequency.     

Buckling and cracking of thin films on compliant substrates under compression

It is shown that unless the substrate is at least as stiff as the film, the energy stored in the substrate contributes significantly to the energy release rate of film delamination under compression either with or without cracking. For very compliant substrates, such as polyethylene terephthalate (PET) with a indium tin oxide (ITO) film, the energy release rate allowing for the deformation of the substrate can be more than an order of magnitude greater than the value obtained neglecting the substrate's deformation. The argument that buckling delaminations tunnel at the tip rather than spread sideways because of increase in mode-mixity may need modification; it is still true for stiff substrates, but for compliant substrates the average energy release rate decreases with delamination width and the limitation in buckled width may be due to this stability as much as the increase in mode-mixity.     

Concomitant wrinkling and buckle-delamination of elastic thin films on compliant substrates

Compressing a thin elastic film attached to a thick compliant substrate can lead to buckling instability. Two commonly observed buckling modes, buckle-delamination and wrinkling, have each been analyzed separately in previous studies. Recent experiments have observed that the two modes can co-exist and co-evolve. In this paper, by analytical and finite element methods, we present a study on concomitant wrinkling and buckle-delamination for an elastic film on a highly compliant substrate. First, without delamination, we present an analytical solution for wrinkling that takes into account the effect of Poisson’s ratio of the substrate. In comparison with a nonlinear finite element analysis, an approximate formula is derived to estimate the normal traction at the interface and to predict initiation of wrinkle-induced delamination. Next, with a pre-existing delamination crack, the critical strain for the onset of buckling instability is predicted by finite element eigenvalue analysis. For an intermediate delamination size, a mixed buckling mode is predicted with the critical compressive strain lower than previous solutions for both wrinkling and buckle-delamination. Post-buckling analyses show a significant shear-lag effect with an effective load transfer length three orders of magnitude greater than the film thickness. Finally, concomitant wrinkling and buckle-delamination is simulated to illustrate the interaction between the two buckling modes, and the results are discussed in view of failure mechanisms and applications in thin film metrology.     

Edge delamination of residually stressed thin films: viscoelastic effects

The theory of interfacial delamination governed by the critical energy release rate criterion is used to predict the initiation of crack growth in thin polyimide films bonded to elastic substrates. The elastic solution for thin films is extended to the viscoelastic case using a correspondence principle valid to the point of initiation of crack growth. A tentative model for decohesion under moisture cycling is proposed to model delayed failure due to exposure to ambient humidity. The effects of relevant parameters such as film thickness and relative humidity are shown for a PMDA/ODA polyimide film bonded to glass.     

Reflection X-ray topography of ZnO thin films on non-orienting substrates

Thin or moderately thick polycrystalline films of ZnO with preferentially oriented crystallites deposited on non-orienting substrates can in some cases be investigated using conventional X-ray topography. Examples of such reflection topographs are presented and their characteristic features are discussed. In particular, it is often possible to observe the texture, the film inhomogeneity and the influence of the deposition conditions on the preferred orientation.     

Electro-fragmentation analysis of dielectric thin films on flexible polymer substrates

An electro-fragmentation method was developed as a fast alternative to the time consuming fragmentation test carried out in situ in a microscope, to investigate the failure of dielectric inorganic coatings on polymer substrates. An ultrathin conductive layer was used to probe the onset of tensile failure in the dielectric coating through changes of its electrical resistance. A careful selection of the conductive layer has been carried out to avoid artifacts resulting for instance from a change of the cohesive properties (e.g. internal stress state) of the investigated structures. Au layers were found to be too ductile, contrary to Al-Ti layers that were too brittle, which invalidated the use of both materials to probe the failure of the dielectric coatings. In contrast, for structures on high-temperature polymer substrates, a 10 nm thick amorphous graphite (a-G) layer was found to accurately reproduce the cracking of the coating. The Young's modulus and coefficient of thermal expansion of the a-G layer are low enough not to impact the internal strain, hence the crack onset strain of the dielectric coating. The a-G layer is also sufficiently brittle, and its cohesive failure and resulting increase of electrical resistance is triggered by the failure of the dielectric coating. The a-G electro-fragmentation method is presently limited to polymers substrates with a glass-transition temperature higher than 100 °C.