Showing papers by "Zhigang Suo published in 2004"

Electronic skin: architecture and components

Abstract: Conceptual hardware architecture of skin-like circuits is described. An elastomeric skin carries rigid islands on which active subcircuits are made. The subcircuit islands are interconnected by stretchable metallization. We concentrate on recent advances in stretchable thin-film conductors, by covering their construction, evaluation, and laboratory and theoretical analysis. Reversibly stretchable conductors with electrically-critical strains ranging from 10% to 100% have been made.

Stretchability of thin metal films on elastomer substrates

Abstract: Many flexible electronic surfaces comprise inorganic films on organic substrates. Mechanical failure of such integrated structures of stiff and compliant materials poses a significant challenge. This letter studies the stretchability of metal films on elastomer substrates. Our experiment shows that, when stretched, elastomer-supported metal films rupture at strains larger than those reported for freestanding films. We use a finite element code to simulate the rupture process of metal films. A freestanding metal film ruptures by forming a single neck. By contrast, a metal film on an elastomer substrate may develop an array of necks before rupture. While the pre-rupture necks do not change the electrical conductance appreciably, they elongate the metal film, leading to a large overall rupture strain.

Design and performance of thin metal film interconnects for skin-like electronic circuits

Abstract: We prepare stretchable electrical conductors of 25-nm-thick gold films on elastomeric substrates prestretched by 15%. When the substrates relax from the prestretch, the gold stripes form surface waves with /spl sim/8.4-/spl mu/m wavelength and /spl sim/1.2-/spl mu/m amplitude. When the strain is cycled between 0 and 15%, both the wave pattern and the electrical resistance of the gold stripes change in reproducible cycles. Such repeatedly stretchable metallization can serve as interconnects for skin-like, conformal, and electroactive polymer circuits.

Partition of unity enrichment for bimaterial interface cracks

Abstract: Partition of unity enrichment techniques are developed for bimaterial interface cracks. A discontinuous function and the two-dimensional near-tip asymptotic displacement functions are added to the finite element approximation using the framework of partition of unity. This enables the domain to be modelled by finite elements without explicitly meshing the crack surfaces. The crack-tip enrichment functions are chosen as those that span the asymptotic displacement fields for an interfacial crack. The concept of partition of unity facilitates the incorporation of the oscillatory nature of the singularity within a conforming finite element approximation. The mixed-mode (complex) stress intensity factors for bimaterial interfacial cracks are numerically evaluated using the domain form of the interaction integral. Good agreement between the numerical results and the reference solutions for benchmark interfacial crack problems is realized. Copyright © 2004 John Wiley & Sons, Ltd.

Stretchable and elastic interconnects

Abstract: The present invention relates to stretchable interconnects which can be made in various geometric configurations, depending on the intended application. The stretchable interconnects can be formed of an electrically conducting film or an elastomer material to provide elastic properties in which the interconnects can be reversibly stretched in order to stretch and relax the elastomer material to its original configuration. Alternatively, stretchable interconnects can be formed of an electrically conducting film or a plastic material to provide stretching of the material to a stretched position and retaining the stretched configuration. The stretchable interconnect can be formed of a flat 2-dimensional conductive film covering an elastomeric or plastic substrate. When this structure is stretched in one or two dimensions, it retains electrical conduction in both dimensions. Alternatively, the stretchable and/or elastic interconnects can be formed of a film or stripe that is formed on an elastomeric or plastic substrate such that it is buckled randomly, or organized in waves with long-range periodicity. The buckling or waves can be induced by various techniques, including: release of built-in stress of the conductive film or conductive stripe; pre-stretching the substrate prior to the fabrication of the conductive film or conductive stripe; and patterning of the surface of the substrate prior to the fabrication of the metal film. The stretchable interconnect can be formed of a plurality of conductive films or conductive stripes embedded between a plurality of layers of a substrate formed of an elastomer or plastic.

Evolution of wrinkles in hard films on soft substrates.

Abstract: A compressively strained film on a substrate can wrinkle into intricate patterns. This Rapid Communication studies the evolution of the wrinkle patterns. The film is modeled as an elastic nonlinear plate and the substrate a viscoelastic foundation. A spectral method is developed to evolve the nonlinear system. When the initial film strains are isotropic, the wrinkles evolve into a pattern with a motif of zigzag segments, in random orientations. When the initial film strains are anisotropic, the wrinkles evolve to an array of herringbones or stripes. The zigzag segments select a width, a length, and an elbow angle that minimize the total elastic energy.

Stretchable wavy metal interconnects

Abstract: Buckled, wavy metal stripes are promising candidates for interconnects in flexible and stretchable electronics. To obtain wavy metal films, 5 nm of Cr (for adhesion) and 20 nm of Au were evaporated on polydimethyl siloxane (PDMS) prestretched by 25%. The metals buckle to a wave upon release of the PDMS from the prestretched position. The electrical resistance of the Au was measured as a function of applied tensile strain. Results show the metal remains electrically conductive up to 100% strain and maintains electrical continuity under repeated mechanical deformation. Presented are the sample fabrication, surface topography, and results of experiments conducted on these stretchable wavy metals.

Spherical deformation of compliant substrates with semiconductor device islands

Abstract: conventional methods on flat foil substrates, into a spherically shaped cap after the device fabrication process. In contrast to rolling, with spherical deformation, the surface is in tension on both the concave and convex sides of the substrate and thinning the substrate cannot be used to reduce the strain. Because inorganic semiconductor materials are brittle, the uniform layers of device materials crack during the substrate deformation. Thus, spherical deformation is fundamentally more difficult than cylindrical deformation because the deformation inherently involves stretching the substrate and devices on it, independent of the substrate thickness. In this article, Sec. II explains our approach to plastically deform thin foil substrates into spherical dome shapes. Section III demonstrates that by patterning device materials into isolated islands, ‘‘hard’’ device islands can remain crack free after deformation. Finally, Sec. IV discusses that the strain distribution in the device islands for two different substrate structures, and why patterning brittle materials into islands suppresses fracture in the devices.

Field-effect mobility of amorphous silicon thin-film transistors under strain

Abstract: We applied strain ranging from 1% compressive to ∼0.3% tensile to a-Si:H TFTs on polyimide foils by bending them inward or outward, or by stretching them in a microstrain tester. We also applied strain to a-Si:H TFTs by deforming a flat substrate into a spherical dome. In each case, compression lowered and tension raised the on-current and hence the electron field-effect mobility. We conclude that compressive strain broadens both the valence and conduction band tails of the a-Si:H channel material, and thus reduces the effective electron mobility. We show that the mobility can be used as an indicator of local mechanical strain.

Effects of mechanical strain on TFTs on spherical domes

Abstract: In this paper, amorphous-silicon (a-Si:H) thin-film transistors (TFTs) were fabricated on a plastic substrate, which was then permanently deformed into a spherical dome shape after the device fabrication process. The TFTs were patterned in an island structure to prevent cracking in the device films during the substrate deformation. In the majority of the TFTs, the off-current and gate leakage current do not change substantially. Depending on the island structure, the electron mobility either increased or decreased after deformation. This change in mobility was correlated with the mechanical strain in the device islands determined by finite element modeling of the deformation process. Tensile strain caused slightly higher mobility in planar structures. In a mesa-type structure, silicon films on top of the pillars could be in compression after the dome deformation, leading to a slight decrease in mobility.

A Continuum Theory That Couples Creep and Self-Diffusion

Abstract: In a single-component material, a chemical potential gradient or a wind force drives self-diffusion. If the self-diffusion flux has a divergence, the material deforms. We formulate a continuum theory to be consistent with this kinematic constraint. When the diffusion flux is divergence-free, the theory decouples into Stokes's theory for creep and Herring's theory for self-diffusion. A length emerges from the coupled theory to characterize the relative rate of self-diffusion and creep. For a flow in a film driven by a stress gradient, creep dominates in thick films, and self-diffusion dominates in thin films. Depending on the film thickness, either stress-driven creep or stress-driven diffusion prevails to counterbalance electromigration. The transition occurs when the film thickness is comparable to the characteristic length of the material.

Electromigration lifetime and critical void volume

Abstract: We study electromigration in copper lines encapsulated in an organosilicate glass. A line fails when a void near the upstream via grows to a critical volume. We calculate the void volume as a function of time. The statistical distribution of the critical volume (DCV) is taken to be independent of testing variables, such as line length and electric current density. By contrast, the distribution of the lifetime (DLT) strongly depends on these testing variables. We deduce the DCV from the experimentally measured DLT. Once deduced, the DCV can predict the DLT under untested conditions.

Programmable motion and patterning of molecules on solid surfaces

Abstract: Adsorbed on a solid surface, a molecule can migrate and carry an electric dipole moment. A nonuniform electric field can direct the motion of the molecule. A collection of the same molecules may aggregate into a monolayer island on the solid surface. Place such molecules on a dielectric substrate surface, beneath which an array of electrodes is buried. By varying the voltages of the electrodes individually, it is possible to program molecular patterning, direct an island to move in a desired trajectory, or merge several islands into a larger one. The dexterity may lead to new technologies, such as reconfigurable molecular patterning and programmable molecular cars. This paper develops a phase field model to simulate the molecular motion and patterning under the combined actions of dipole moments, intermolecular forces, entropy, and electrodes.

Experimental Determination of Crack Driving Forces in Integrated Structures

Abstract: For a crack in a structure, the crack driving force G is the reduction of the elastic energy in the structure, associated with the crack extending per unit area. In principle, G can be calculated by solving a boundary value problem. In practice, however, such a calculation is prohibitively difficult for integrated structures of complex architectures, diverse materials and small features. The calculated G is suspect when deformation properties and residual stress fields are poorly characterized. On the other hand, it costs little to make many replicates of an integrated structure, so that massive testing is affordable. We describe an experimental method to measure G. A crack, assisted by molecules (e.g., moisture) in the environment, often extends at a velocity V increasing with the crack driving force G. The V-G function is specific to a given material and its environment. Once determined, the same function applies when this material is integrated in a structure with other materials, provided environmental molecules reach the crack front. In the integrated structure, an observed crack velocity, together with the known V-G function, provides a reading of the crack driving force. The observed crack velocity can be used to measure deformation properties of ultrathin films. We also describe a procedure to measure the crack driving force GR due to the residual stress field in the integrated structures, even when GR by itself is too low for the crack to extend at a measurable velocity.

Time-dependent crack behavior in an integrated structure

Abstract: Devices in modern technologies often have complex architectures, dissimilar materials, and small features. Their long-term reliability relates to inelastic, time-dependent mechanical behavior of such structures. This paper analyzes a three-layer structure consisting of, from top to bottom, an elastic film, a power-law creep underlayer, and a rigid substrate. The layers are bonded. Initially, the film is subject to a uniform biaxial tensile stress. A channel crack is introduced in the elastic film. As the underlayer creeps, the stress field in the film relaxes in the crack wake, but intensifies around the crack tip. We formulate nonlinear diffusion-like equations that evolve the displacement field. When the crack is stationary, the region in which the stress field relaxes increases with time. We identify the length scale of the region as a function of time. The stress intensity factor is proportional to the square-root of the length scale. For the power-law creep underlayer, this newly identified length depends on the film stress, and corrects an error in a previous paper by Huang, Prevost and Suo (Acta Materialia 50, 4137, 2002). When the crack advances, its velocity can reach a steady state. We identify the scaling law for the steady velocity. An extended finite element method (X-FEM) is used to simultaneously evolve the creep strain and crack length. Numerical results are presented for the stress intensity factors of stationary cracks, and the steady velocities of advancing cracks.

Nanoscale Domain Stability in Organic Monolayers on Metals

Abstract: Certain organic molecules, such as alkanethiols, can adsorb On metals to form monolayers. Sometimes domains appear in the monolayers. For example, an incomplete monolayer may form islands, and a mixed-composition monolayer may separate into distinct phases. During annealing, the molecules diffuse on the metal surface. The domain boundary energy drives the domains to coarsen. The contact potential between the dissimilar domains drives the domains to refine. On the basis of existing experimental information, we suggest that the competition between coarsening and refining should stabilize certain domain patterns. We formulate a free energy functional to include the effects of mixed species, domain boundary, and contact potential. An approximate energy minimisation estimates the equilibrium domain size. We derive a diffusion equation consistent with the free energy functional. The numerical solution of the diffusion equation follows the evolution of the monolayers from a random initial concentration field to patterns of dots and stripes. We also discuss the practical implications of the theory and, in particular the possibility of guided self-assembly.

Statistics of Electromigration Lifetime Analyzed Using a Deterministic Transient Model

Abstract: The electromigration lifetime is measured for a large number of copper lines encapsulated in an organosilicate glass low-permittivity dielectric. Three testing variables are used: the line length, the electric current density, and the temperature. A copper line fails if a void near the upstream via grows to a critical volume that blocks the electric current. The critical volume varies from line to line, depending on line-end designs and chance variations in the microstructure. However, the statistical distribution of the critical volume (DCV) is expected to be independent of the testing variables. By contrast, the distribution of the lifetime (DLT) strongly depends on the testing variables. For a void to grow a substantial volume, the diffusion process averages over many grains along the line. Consequently, the void volume as a function of time, V(t), is insensitive to chance variations in the microstructure. As a simplification, we assume that the function V(t) is deterministic, and calculate this function using a transient model. We use the function V(t) to convert the experimentally measured DLT to the DCV. The same DCV predicts the DLT under untested conditions.

Experimental Determination of Crack Driving Forces in Integrated Structures

Abstract: For a crack in a structure, the crack driving force G is the reduction of the elastic energy in the structure, associated with the crack extending per unit area. In principle, G can be calculated by solving a boundary value problem. In practice, however, such a calculation is prohibitively difficult for integrated structures of complex architectures, diverse materials and small features. The calculated G is suspect when deformation properties and residual stress fields are poorly characterized. On the other hand, it costs little to make many replicates of an integrated structure, so that massive testing is affordable. We describe an experimental method to measure G. A crack, assisted by molecules (e.g., moisture) in the environment, often extends at a velocity V increasing with the crack driving force G. The V‐G function is specific to a given material and its environment. Once determined, the same function applies when this material is integrated in a structure with other materials, provided environmental molecules reach the crack front. In the integrated structure, an observed crack velocity, together with the known V‐G function, provides a reading of the crack driving force. The observed crack velocity can be used to measure deformation properties of ultrathin films. We also describe a procedure to measure the crack driving force GR due to the residual stress field in the integrated structures, even when GR by itself is too low for the crack to extend at a measurable velocity.