Buckling Of Thin Film Research Articles

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.

Water nanolayer facilitated solitary-wave-like blisters in MoS2 thin films

Solitary waves are unique in nonlinear systems, but their formation and propagation in the nonlinear fluid-structure interactions have yet to be further explored. As a typical nonlinear system, the buckling of solid thin films is fundamentally related to the film-substrate interface that is further vulnerable to environments, especially when fluids exist. In this work, we report an anomalous, solitary-wave-like blister (SWLB) mode of MoS2 thin films in a humid environment. Unlike the most common telephone-cord and web buckling deformation, the SWLB propagates forward like solitary waves that usually appear in fluids and exhibits three-dimensional expansions of the profiles during propagation. In situ mechanical, optical, and topology measurements verify the existence of an interfacial water nanolayer, which facilitates a delamination of films at the front side of the SWLB and a readhesion at the tail side owing to the water nanolayer-induced fluid-structure interaction. Furthermore, the expansion morphologies and process of the SWLB are predicted by our theoretical model based on the energy change of buckle propagation. Our work not only demonstrates the emerging SWLB mode in a solid material but also sheds light on the significance of interfacial water nanolayers to structural deformation and functional applications of thin films.

FEM Analysis of Buckled Dielectric Thin-Film Packaging Based on 3D Direct Numerical Simulation.

This paper presents a 3D direct numerical simulation of buckled thin-film packaging based on transferred elastic thin-film wrinkling bonded on a compliant polymer ring. The mode change of the fabricated thin-film cap is found by measuring the thin-film cap shape at different times after Si substrate debonding. The conventional linear and nonlinear buckling simulations are not adequate to understand the behavior of the thin-film buckling mechanism creating such packaging cap mode change. Direct buckling simulation is recently reported as an easy and useful numerical wrinkling simulation method. A novel 3D FEM model of a thin-film package suitable for direct 3D buckling simulation is built to reduce the mode mixture between different buckling modes. Buckling modes of the packaging cap are investigated in terms of elastic moduli of package materials and applied strain due to thermal expansion coefficient difference. Based on the simulation results, it is found that there are two main modes in the fabricated thin-film buckling package determining the shape of the transferred thin-film packaging cover depending on the elasticity ratio between the cap and sealing ring materials. The mode shift from wrinkling cap mode to out-of-plane cap mode due to applied strain along a polymeric sealing ring is found.

Pressure and folding effects on the buckling of a freestanding compressed thin film.

The combined effects of compressive stress, applied pressure, and edge folding of a freestanding thin film have been theoretically investigated on the buckle morphologies of the structure. In the framework of the Föppl-von Kármán theory of thin plates, the different buckle profiles have been analytically determined, and two buckling regimes have been identified for the film: one regime where the transition from upward to downward buckling is continuous, and one that is discontinuous (snap-through). The critical pressures characterizing the different regimes have then been determined, and an hysteresis cycle has been identified through the study of buckling versus pressure. The case in which the thin film is deposited on a substrate has also been discussed.

Swelling-induced pattern transformations of periodic hydrogels — from the wrinkling of internal surfaces to the buckling of thin films

We investigate pattern transformations of periodic hydrogel systems that are triggered by swelling-induced structural instabilities. The types of microstructures considered in the present work include single-phase and two-phase voided hydrogel structures as well as reinforced hydrogel thin films. While the observed transformations of the single-phase structures show good agreement with experimental findings, the two-phase materials provide novel patterns associated with wrinkling of internal surfaces. Furthermore, an extensive parametric study on the reinforced hydrogel thin films reveals new opportunities for the design of complex out-of-plane surface modes caused by swelling-induced instabilities. Next to the mentioned buckling-type instabilities, we encountered the development of micro-creases at the internal surfaces of periodic media.

Compression-induced buckling of thin films bonded to viscous substrates: Uniform wrinkles vs localized ridges

We examine the buckling of a thin elastic film bonded to a much thicker viscous substrate undergoing compression at a fixed rate. Experiments show two distinct buckling modes. At high rate of compression or at large liquid thickness, the buckles take on the form of approximately-sinusoidal wrinkles. At low rate of compression or at small liquid thickness, the buckles are highly localized into tall ridges separated nearly flat regions. Ridge growth is accompanied by lateral motion of the film in the near-ridge region, and the liquid in that region undergoes severe shear flow. Such ridge formation is entirely distinct from other examples of curvature localization such as fold localization of films on liquids in static equilibrium or ridge formation of films bonded to hyperelastic substrates. We quantify how the two lengthscales that arise from the buckling process, the wrinkle amplitude and the interridge distance, depend on compression rate and liquid thickness. We show that wrinkles formed during compression can also transform into ridges under quiescent conditions which suggests that buckle localization reduces bending energy of the film. We speculate that ridge localization appears due to a competition between two effects: a buckle mode with a few well-spaced ridges offers a lower energy state than uniform wrinkles, but wrinkles can develop faster because they require the viscous fluid to move over shorter distances.

Monolithic elliptical dome Fabry–Perot microcavities exhibiting large birefringence

We report on the experimental and theoretical characterization of elliptically shaped Fabry–Perot microcavities fabricated through a controlled thin-film buckling process. Due to the highly astigmatic nature of the buckled mirrors, the cavity modes are well described as elliptical Hermite–Gaussian beams. In addition to lifting the typical degeneracy of higher-order transverse spatial modes, the cavities exhibit large polarization-mode splitting greater than 25 GHz in the 1550 nm wavelength range. This large, controllable, and highly predictable birefringence makes these cavities of interest for emerging applications in cavity quantum optics that rely on non-degenerate polarization modes.

Controlled Bi-Axial Buckling and Postbuckling of Thin Films Suspended on a Stretchable Substrate with Square Prism Relief Structures

Stretchable electronics have spurred rapid developments from curvilinear devices to bio-integrated diagnostic and therapeutic devices. The wavy configuration in the device components on a stretchable elastomeric substrate surface plays a prominent role in simultaneously achieving high areal coverage and stretchability without compromising the electric performance, resulting in unique applications in stretchable and flexible light-emitting diodes (LEDs), batteries, supercapacitors, and photovoltaics. In this study, we investigate the buckling behaviors of stiff thin films on the top surface of a biaxially pre-strained elastomeric substrate with square prism micro-patterned structures. Based on energy minimization, a theoretical model is established to study the buckling profiles and the maximum strain for different pre-strain levels along two directions, which agrees reasonably well with those obtained by the finite element analysis (FEA). After revealing the effect of the center-to-center distance in micro-patterned structures and the interfacial contact width between the film and substrate on the buckling behavior, the elastic stretchability of the system is studied.

Pressure sensing with high-finesse monolithic buckled-dome microcavities.

We describe the use of on-chip buckled-dome Fabry-Perot microcavities as pressure sensing elements. These cavities, fabricated by a controlled thin-film buckling process, are inherently sealed and support stable optical modes (finesse >103), which are well-suited to coupling by single-mode fibers. Changes in external pressure deflect the buckled upper mirror, leading to changes in resonance wavelengths. Experimental shifts are shown to be in good agreement with theoretical predictions. Sensitivities as large as ∼1nm/kPa, attributable to the low thickness (<2µm) of the buckled mirror, and resolution ∼10Pa are demonstrated. We discuss potential advantages over traditional low-finesse, quasi-planar Fabry-Perot pressure sensors.

In situ characterization of buckling dynamics in silicon microribbon on an elastomer substrate

Buckling of rigid thin films on elastomer substrates underlies the fabrication foundation of stretchable soft electronics. Here we demonstrate an optical approach to in situ characterize the buckling of silicon microribbon driven by releasing the pre-stretched poly-dimethylsiloxane (PDMS) substrate at a controllable strain rate. The method, based on quantitative differential interference microscopy, directly captures the space–time evolution of the surface topography at a frame rate of 100 fps in a large field of view of 50 × 195μm2. The nucleation, propagation and stabilization of the buckled structure during the buckling and unbuckling processes are observed and quantified. Our experiment reveals that a sequence of partially buckled patterns are energetically stable to bridge the unbuckled and fully buckled states. This work opens a new experimental scheme for the research on stretchable soft electronics and provides new evidence for the theoretical study of the buckling dynamics.

Dynamic stability analysis of stiff films by element-free method with strain-rotation decomposition

Buckling and post-buckling analysis of thin films is significant for the design, optimization and fabrication of stretchable electronic devices based on compression buckling. Aiming to achieve a more accurate and reliable way for the dynamic stability analysis of stiff films considering geometric nonlinearity, an implicit dynamic element-free Galerkin method based on the Strain-Rotation decomposition theorem is developed in this paper to investigate the dynamic buckling behavior of stiff films. Convergence and comparison studies are conducted to validate the numerical stability and accuracy of the proposed numerical method. The influences of compression loading rate and thickness to length ratio on the buckling/post-buckling of stiff thin films subjected to dynamic load are numerically analyzed and discussed in parametric studies. This work provides an effective way for the engineering computation of flexible electronic technology.

Grain boundary-induced plasticity during thin film buckling

The effect of grain boundaries (GB) on the buckling of an Al thin film delaminated from its substrate is investigated by means of molecular dynamics simulations at finite temperature. It is evidenced that the GB localizes the plasticity and deeply modifies the profile of the buckled thin film through the formation of a vertical fold at the location of the initial GB. Several plasticity mechanisms have been also described such as the development of extrinsic faults or the formation of uncommon C’D and CD’ dislocations. In this context, the folding angle and plastic strain in the film have been analyzed through a careful counting of the emerging dislocations at the film surfaces. The buckling profile of the film has been then analytically determined in the framework of the Föppl–von Karman’s (FvK) theory of thin plates and successfully compared with the simulated ones. The modifications of the film pattern in light of the different plastic (dislocations) and elastic (buckling) phenomena are finally discussed.

Dynamic Behaviors of Postbuckled Thin Film on Flexible Substrates Considering Viscoelastic Effects

AbstractStretchable electronic systems based on controllable compressive buckling can be further endowed with superior compliance and stretchability. However, such systems are usually restrained by the interference from different loads in practical applications, so it is desirable to study their dynamic behaviors. In this article, an analytical model is developed on the linear free vibrations of a buckled thin film attached to a flexible substrate, whose results can be verified by the finite element analysis (FEA). In the model, the film is considered as an Euler–Bernoulli beam, and the substrate is assumed as a Pasternak foundation with Kelvin viscoelasticity. The natural frequencies and their corresponding vibration modes of the buckled film with the substrate are obtained. The results indicate that the increases of stiffness and damping of the substrate have negative effects on the natural frequencies. The damping influences the low-order modes a lot but not the high-order modes. This study may provide some suggestions for the dynamic design of buckled thin films on flexible substrates. For example, the controllable vibration attenuation can be achieved by choosing the substrate with appropriate viscoelasticity.

Microstructural Effects on the Interfacial Adhesion of Nanometer-Thick Cu Films on Glass Substrates: Implications for Microelectronic Devices.

Improving the interface stability for nanosized thin films on brittle substrates is crucial for technological applications such as microelectronics because the so-called brittle–ductile interfaces limit their overall reliability. By tuning the thin film properties, interface adhesion can be improved because of extrinsic toughening mechanisms during delamination. In this work, the influence of the film microstructure on interface adhesion was studied on a model brittle–ductile interface consisting of nanosized Cu films on brittle glass substrates. Therefore, 110 nm thin Cu films were deposited on glass substrates using magnetron sputtering. While film thickness, residual stresses, and texture of the Cu films were maintained comparable in the sputtering processes, the film microstructure was varied during deposition and via isothermal annealing, resulting in four different Cu films with bimodal grain size distributions. The interface adhesion of each Cu film was then determined using stressed Mo overlayers, which triggered Cu film delaminations in the shape of straight, spontaneous buckles. The mixed-mode adhesion energy for each film ranged from 2.35 J/m2 for the films with larger grains to 4.90 J/m2 for the films with the highest amount of nanosized grains. This surprising result could be clarified using an additional study of the buckles using focused ion beam cutting and quantification via confocal laser scanning microscopy to decouple and quantify the amount of elastic and plastic deformation stored in the buckled thin film. It could be shown that the films with smaller grains exhibit the possibility of absorbing a higher amount of energy during delamination, which explains their higher adhesion energy.

Buckle-Delamination-Enabled Stretchable Silver Nanowire Conductors.

Controlled buckling and delamination of thin films on a compliant substrate has attracted much attention for applications ranging from micro/nanofabrication to flexible and stretchable electronics to bioengineering. Here, a highly conductive and stretchable conductor is fabricated by attaching a polymer composite film (with a thin layer of silver nanowires embedded below the surface of the polymer matrix) on top of a prestretched elastomer substrate followed with releasing the prestrain. A partially delaminated wavy geometry of the polymer film is created. During the evolution of the buckle-delamination, the blisters pop-up randomly but self-adjust into a uniform distribution, which effectively reduces the local strain in the silver nanowires. The resistance change of the conductor is less than 3% with the applied strain up to 100%. A theoretical model on the buckle-delamination structure is developed to predict the geometrical evolution, which agrees well with experimental observation. Finally, an integrated silver nanowire/elastomer sensing module and a stretchable thermochromic device are developed to demonstrate the utility of the stretchable conductor. This work highlights the important relevance of mechanics-based design in nanomaterial-enabled stretchable devices.

Self-transformed parallel structures in strain sensitive Au thin film micropattern embedded on soft elastomer

This work presents a self transformed method of ordering random buckles in thin metal film fabricated on soft elastomeric film for reliable MEMS devices. Detailed modeling of thin metal film buckling and buckle manipulative stresses associated with the self transformed film is investigated. In this study, a thin metal Au film deposited with dc sputtering is used as a strain sensing film on an elastomeric of polydimethylsiloxane (PDMS) film. To increase the adhesion between the metal film and underlying PDMS film, a self-assembled molecular adhesive layer of (3-mercaptopropyl)trimethoxysilane (MPTMS) has been introduced. The random buckles developed in the Au film were successively oriented without using any ridge surface and prestrain PDMS film for the first time. The strain response study of the Au thin-film resistors of different thicknesses has been characterized for determining the normalized variation of resistance for linear operation. The experimental result showed that the Au thin film resistor on PDMS has high strain sensitivity compared to Au film on Si. The microscopic study of the Au thin film resistor confirmed that the observed high resistance change is due to the micro/nanocracks near grain boundaries on the thin Au film. This study is beneficial for ordering random buckles in hybrid thin-film microstructure on soft elastomer material and fabricating high strain sensitive MEMS devices.

Instability driven surface patterns: Insights from direct three-dimensional finite element simulations

Surface patterns driven by mechanical instability commonly form in thin-film structures with a compliant substrate. In this study a practical three-dimensional (3D) finite element modeling approach is employed to directly simulate surface instabilities. It is based on our previously developed embedded imperfection technique in two-dimensions, and is now successfully implemented in 3D to capture sinusoidal wrinkling under uniaxial compression and the checkerboard pattern under equi-biaxial compression. The numerical approach overcomes typical challenges in computationally modeling thin-film buckling instability without the need of sophisticated treatment. The simulation results show that instability-controlled surface patterning is not an instantaneous process. A local disturbance in deformation originates from the imperfection site and propagates outward, eventually leading to a uniform pattern across the entire surface.

Quantification of the Influence of Thin Film Microstructure on Adhesion for a Model Brittle-Ductile Interface

The influence of film microstructure on interface adhesion was studied on a model brittle-ductile interface consisting of thin Cu films on brittle glass substrates. Therefore, 110 nm thin Cu films were deposited on glass substrates using magnetron sputtering. While film thickness, residual stresses, and texture of the Cu films were maintained comparable in the sputtering processes, the film microstructure was varied during deposition and via isothermal annealing resulting in four different Cu films with bimodal grain size distributions. The interface adhesion of each Cu film was determined using stressed Mo overlayers, which triggered delamination of the Cu film from the glass substrates in the shape of straight spontaneous buckles. The model of Hutchinson and Suo for spontaneous buckles was applied to quantify the mixed mode adhesion energy for each film system ranging from 2.35 J/m² for the films with the highest amount of large grains to 4.90 J/m² for the films with the highest amount of nanosized grains. This surprising result could be clarified using an additional study of the buckles using focused ion beam cutting and quantification via confocal laser scanning microscopy to decouple and quantify the amount of elastic and plastic deformation stored in the buckled thin film. It could be shown that the films with smallest grains exhibit the possibility to absorb a higher amount of energy during delamination, which explains their improved adhesion.

Circumferential buckling and postbuckling analysis of thin films integrated on a soft cylindrical substrate with surface relief structures

As a novel tactic, controlled buckling of the stiff thin film device component on a compliant substrate with surface relief structures has been widely explored in the design and demonstration of various flexible and stretchable electronic devices. While flat substrates are mainly used in the current design and demonstration of the buckled thin film on a structured substrate, the use of cylindrical substrates presents alternative opportunities for this technique with direct applications in multifunctional catheters for the treatment of ventricular tachycardia, primary and metastatic malignancies, as well as various smart wearable devices. In this study, we will present the modeling analysis and design considerations of thin film device components on a soft cylindrical substrate with surface relief structures. By investigating the controlled circumferential buckling and postbuckling behaviors of stiff thin film integrated on a compliant cylindrical substrate with surface relief structures, the buckling/postbuckling amplitude and maximum strain in the thin film are found to depend on various material and geometric parameters. Additionally, the results predicted from the analytic model are validated by the finite element analysis, which provides a powerful toolset to inform experimental designs.

Buckling of a stiff thin film on a bi-layer compliant substrate of finite thickness

The buckling of a stiff thin film on a compliant substrate has been widely studied over the past decade due to its wide applications such as stretchable electronics, micro- and nano-metrology, and surface engineering. Instead of a single-layer compliant substrate, a bi-layer compliant substrate is usually encountered in practical applications. In this paper, the buckling of a stiff thin film on a bi-layer compliant substrate of finite thickness is studied theoretically, numerically and experimentally. The theoretical models based on the small-deformation theory and the simple finite-deformation theory accounting for the geometry change by using the energy method are both developed and presented. The good agreement among theoretical predictions, finite element analysis and experimental measurements of the buckling behavior validates the theoretical model. The influences of finite thickness of the bi-layer substrate and substrate modulus ratio on the buckling wavelength and critical buckling strain are systematically investigated. The buckling configurations at various applied strains are also measured to further validate the theoretical model. These results shed light on the influence of finite substrate thickness on buckling of the bi-layer substrate-supported thin films and are helpful to provide design guidelines in practical applications.