Interface Corner Research Articles

Generation and elimination of silicon pitting for 300 mm CMOS process technologies

The complementary metal oxide semiconductor (CMOS) process technology in a 300 mm wafer fab experienced wafer center yield loss. In-line wafer defect inspection revealed gross silicon pitting at the wafer center as the root cause of the yield loss. Affected dies showed pitting at the interfacial corner between the silicon substrate and the isolation oxide. The mechanism of silicon pitting involves creation of silicon microdefects during several high-temperature furnace anneal process steps (liner oxide and posthigh energy phosphorus implant anneals) because of local die and global wafer level thermally induced mechanical stress at the silicon substrate to isolation oxide interfacial corner. In addition, implant-induced silicon microdefects from a high energy (>2 MeV) phosphorus implant, extending to the silicon surface provide a further significant contribution to the silicon microdefect population. The overall microdefect population is further aggravated by Ostwald ripening during a subsequent thick silicon-oxide furnace growth process, resulting in sufficient corner silicon microstructure damage to enhance wet-etching during a subsequent wet-clean leading to gross silicon pitting. Silicon pitting is eliminated by lowering either the liner oxide or postimplant anneal temperatures or skipping the high energy phosphorus implant. Incorporating a reduced liner oxide anneal temperature into the CMOS process flow eliminated the wafer-level yield loss at the wafer center associated with gross silicon pitting defects.

Fracture initiation in bi-material joints subject to combined tension and shear loading

Linear elastic solution of the stress field near an interface corner of bi-material joints is of the form Hrλ−1, where r is the radial distance from the corner, H is the stress intensity factor and λ–1 is the order of the singularity. Finite element analysis is used to determine the magnitude of H for a butt joint subject to remote shear; the obtained solution complements existing solution for remote tension and uniform change in temperature. The theoretical solution of the singular shear stress is shown to be in good agreement with the corresponding finite element solution. The effect of combined remote tension, remote shear and uniform change in temperature on the failure loads and failure mechanisms is experimentally determined for brass/araldite/brass butt joint. It is shown that the failure envelope in tensile stress – shear stress space is elliptical and the failure loads decrease with increasing cure temperature due to thermal residual stress associated with the curing process. The application of the results to the assessment of onset of failure in composite patch repair is discussed.

How to obtain the adhesive strength for double lap joint by using single lap joint

The testing method of adhesive strength of lap joint is prescribed in Japanese Industrial Standard (JIS K6850). However, it has been reported that the strength of double lap joint (DLJ) is about two times larger than the one of single lap joint (SLJ). Therefore, suitable testing method has been required from industries. In this study, the equivalent conditions of strength for SLJ and DLJ are investigated in terms of the intensity of singular stress field (ISSF) appearing at the interface end. First, in order to minimize the bend effect for SLJ, the effect of the specimen geometry on ISSF and deformation angle at the interface corner is considered under the same adhesive geometry and load P. It is found that the minimum ISSF of SLJ can be obtained when the adherend thickness t1 is large enough, and the deformation angle at interface corner is also smallest when adherend thickness t1 is large enough. Therefore, it is necessary to use the specimen with thicker adherend thickness. Then, the equivalent conditions of strength for SLJ and DLJ is investigated by changing adherend thickness. The results show that the strength of the DLJ in JIS ( t1 = 1.5mm) can be obtained by using the SLJ with adherend thickness t1 = 7mm. When the adherend thickness t1 ≥ 25mm, the strength of SLJ is nearly equal to that of DLJ.

Acoustic valley states and acoustic valley transport in sonic crystals

We report the discovery of acoustic valley states in sonic crystals and the observation of the valley transport in the domain walls. The concept of valley pseudospin, labeling quantum states of energy extrema in momentum space, is attracting attention for its potential as a new type of information carrier. Inspired by the recent valley related phenomenon in election systems, the acoustic version of valley states in sonic crystals is studied and the vortex nature of such states is revealed. The extraordinary chirality of valley vortex states may provide new possibilities in sound manipulations and will be appealing to scalar acoustics since the absence of spin degree of freedom here. We further experimentally observe the topological valley transport of sound in sonic crystals. The acoustic valley transport is confined in the domain walls of the sonic crystals and behaves negligible reflection to the interface corners. The acoustic valley transport of sound, strikingly different from that in traditional sound waveguides, may serve as the basis for designing devices with unconventional functions.

Experimental and numerical investigation of the interfacial strength of bi-material joints

An integrated experimental and numerical investigation is employed to examine the interfacial strength of bi-material bonded joints with the aim to quantify the influence of three-dimensional (3-D) stress singularity. The stress singularities at 3-D interface corners and edges have been investigated numerically using finite element methods (FEM). It is found that the effect of the vertex angle on the order of stress singularity at interface corner can be eliminated by smoothing the intersection of interface edges, which can be achieved simply by generating a circular-arc fillet at the intersection of the two free side surfaces. Motivated by this, four-point flexure experiments of bi-material bonded joints, both with and without circular-arc fillet, are conducted. The experimental results suggested that, with a circular-arc fillet design, the strength of the joints may be increased due to the disappearance of 3-D stress singularity at interface corner. Finally, based on an analysis of the intensity of the singularity, an empirical equation that describes the relationship between the failure stress and the largest value of tress singularity order −λ at 3-D interface was determined to predict the interfacial strength of brittle bonded joints.

Cohesive detachment of an elastic pillar from a dissimilar substrate

The adhesion of micron-scale surfaces due to intermolecular interactions is a subject of intense interest spanning electronics, biomechanics and the application of soft materials to engineering devices. The degree of adhesion is sensitive to the diameter of micro-pillars in addition to the degree of elastic mismatch between pillar and substrate. Adhesion-strength-controlled detachment of an elastic circular cylinder from a dissimilar substrate is predicted using a Dugdale-type of analysis, with a cohesive zone of uniform tensile strength emanating from the interface corner. Detachment initiates when the opening of the cohesive zone attains a critical value, giving way to crack formation. When the cohesive zone size at crack initiation is small compared to the pillar diameter, the initiation of detachment can be expressed in terms of a critical value Hc of the corner stress intensity. The estimated pull-off force is somewhat sensitive to the choice of stick/slip boundary condition used on the cohesive zone, especially when the substrate material is much stiffer than the pillar material. The analysis can be used to predict the sensitivity of detachment force to the size of pillar and to the degree of elastic mismatch between pillar and substrate.

三次元異方性異種材接合角部の特異応力場解析

We proposed a new technique to analyze the asymptotic solution around a three dimensional interface corners. We analyzed the scalar parameters of the asymptotic solutions using the H-integral, which is a conservative integral, in conjunction with the finite element analysis. Singular orders of these three-dimensional corners were obtained using the finite element method for the eigen analysis. If λ is an eigen value of a three dimensional corner, -λ-1 is also an eigen value. Complementary eigen values and eigen vectors are used for the H-integral analysis to obtain the scalar parameters. If we select the eigenvalue, -λ-1, as the complementary eigenvalue for the H-integral, the H-integral corresponds with a scalar parameter of the asymptotic solution. We proposed the normalization of the eigenvalues for defining the obtained scalar parameters as the unique values. We demonstrate that the obtained asymptotic solutions correspond well with the stress field obtained by the finite element analyses around three-dimensional interface corners.

Development and application of the integrated sealant test apparatus for sealing gaskets in tunnel segmental joints

An innovative apparatus has been developed in this study to investigate the coupled leakage and mechanical behaviors of gasketed segmental joints, subjected to the field loading conditions during the construction and operation stages. The basic principles and detailed configurations of this newly developed test setup are presented in detail. The test apparatus can be used to accurately monitor the water leakage pressure of segmental joints under various combinations of joint openings and offsets. A series of test sets, based on different characteristics of sealing gaskets used in segmental joints, were subsequently conducted to evaluate the functionality of the test setup. Testing apparatus was designed to evaluate the waterproof capacity of the three types of segmental joints (i.e., longitudinal/circumferential joint and T-joint (intersection of longitudinal and circumferential joints)) in the Nanjing Weisan Rd. Tunnel. The tested segments were cast with the identical gasket groove details and flanks to the practical tunnel segments. The correlation between gasket contact stress and supplied water pressure was analyzed. Comparison of the gasket sealant and mechanical behavior showed that there existed a “correlated zone”. The results showed that gasket-gasket interface, gasket-concrete gasket groove interface, damaged zones, and frame corners were the potential places of leakage in segmental joints. Finally, the results demonstrated that local concrete damages around the groove flank could serve as a water leakage channel and reduced the sealant performance of gasket.

Stress intensity factor analysis of a three-dimensional interfacial corner between anisotropic piezoelectric multi-materials under several boundary conditions on the corner surfaces

Asymptotic solutions around an interfacial corner can be obtained by a combination of the Stroh formalism and the Williams eigenfunction method. The H-integral method, which is derived from Betti’s reciprocal theorem, is useful for analyzing the stress intensity factors (SIFs) of cracks and corners. By expanding these theories for a three-dimensional interfacial corner between anisotropic piezoelectric multi-materials, we develop a modified H-integral method. This method has high generality that can deal with a jointed corner with a varied number of materials and boundary conditions on corner surfaces. We proposed a new definition for the SIFs of an interfacial corner between anisotropic piezoelectric multi-materials, which is compatible with the SIF definitions of a crack in a homogeneous material and an interfacial crack, as well as applicable in various coordinate systems. The accuracy of obtained SIFs was confirmed by comparing the asymptotic solutions obtained from the SIFs with the stress/electric-displacement field directly obtained by the finite element method (FEM). We also propose a numerical method for degenerate materials, which cause numerical problems in the Stroh formalism.

Effect of confinement and interfacial adhesion on peeling of a flexible plate from an elastomeric layer

The finite element method and a cohesive zone model are used to analyze plane strain interfacial debonding of an elastomeric layer from an overhanging deformable plate when it is peeled off by applying a normal displacement at the edge of the overhang. The commercial software, ABAQUS, is employed in this work that is focused on understanding the collective role of the following two non-dimensional parameters: (i) the confinement parameter, α, defined in terms of the flexural rigidity of the plate, and the modulus and the thickness of the interlayer, and (ii) the adhesion parameter, ϕ, defined in terms of the cohesive zone parameters and the modulus to thickness ratio of the interlayer. The interfacial adhesion is characterized by a bilinear traction-separation (TS) relation. Numerical experiments reveal that when α is greater than αc, damage initiates at an interior point on the interface and at the interface corner on the traction-free edge irrespective of the value of ϕ. However, ϕ must be greater than ϕc for the debonding to become wavy/undulatory. The critical value, ϕc, of the adhesion parameter agrees with the necessary condition found in our previous work on debonding of an elastomeric layer from a rigid block when it is uniformly pulled outward. For α < αc, damage/debonding initiates only from the interface corner, and no wavy debonding ensues. The peak peeling force prior to the initiation of an internal debond is found to be a monotonically increasing function of ϕ/α, suggesting its potential use as a design variable and as a guide for determining the TS parameters. Results of a few additional numerical experiments in which the elastomeric layer can debond from both adherends provide insights into designing a demolding process for a sandwiched elastomeric layer.

Effect of stress concentration on plastic deformation of Zr41.2Ti13.8Cu12.5Ni10Be22.5 bulk metallic glass under compressive loading

The influence of different sources of stress concentration on the plastic deformation of the Zr41.2Ti13.8Cu12.5Ni10Be22.5 metallic glass during room temperature compression tests is evaluated. Stress concentration introduced by sample geometry has a significant effect on the mechanical properties: in contrast to the specimen with square cross-section, which shows negligible plastic deformation, a substantial improvement in the plasticity can be achieved for the sample with round cross-section. Simulations of the stress distribution during the compression tests reveal that the stress concentration at the interface corners is responsible for the early fracture of the sample with square cross-section. Additionally, stress concentration during compression tests in the samples with square cross-section can be significantly reduced, and plastic deformation can be enhanced, by removing the interface corners as well as by reducing the friction arising between loading platens and specimen.

Enriched finite element method for three-dimensional viscoelastic interface crack problems

The enriched finite element method is developed for three-dimensional problems of an interface crack between elastic and viscoelastic (including dissimilar viscoelastic) materials. According to the displacement fields of elastic interface crack, the displacement fields of viscoelastic interface crack are derived through the correspondence principle. By incorporating the displacement expressions into the displacement model of regular element, the incremental formulations of enriched element are derived. The stress intensity factors and strain energy release rates can be solved based on the enriched degree of freedoms. A 3-D through interface crack at the center of jointed dissimilar viscoelastic plate subjected to remote tension and a quarter-circular viscoelastic interface corner crack subjected to uniform thermal loading was investigated using the enriched finite element method. It is shown that the present solutions are consistent with the analytical solutions, which indicates the present method is correct and efficient.

接合丸棒の引張りと曲げの解析および特異応力場の強さの比較

In this paper, the stress field at the interface corner edge of a bonded cylinder under bending is discussed by comparing with that under tension. Asymptotic description of the stress field under the bending consists of the singular stress term and the non-singular stress term as well as that under the tension. The similarity relation between the singular stresses under the tension and the bending is confirmed by performing 3D FE analyses on the bonded cylinders under the tension and the bending which are subdivided by the same mesh pattern. The ratios of the intensity of the singular stress field under the bending to that under the tension are computed changing material combinations variously, the maximum and minimum values of the ratios are shown in the table and the chart according to Dundurs' parameter (α,β). The intensity of singular stress field for the bonded cylinder cannot be controlled by Dundurs' parameter uniquely. However, because the differences between the maximum and minimum values are small, the ratios can be controlled by Dundurs' parameter. Then, the ratios are larger than 0.7 and smaller than 1.0 in almost all material combinations with α(α-2β) < 0.

接着剤の強度を合理的に評価する試験法について

In this study, a suitable evaluation method of adhesive strength is investigated focusing on the intensity of singular stress field appearing at the end of interface. The effect of specimen geometry on the intensity of singular stress is considered by changing tensile force direction and fixed boundary length. It is found that the minimum intensity of singular stress can be obtained when the adherend thickness is large enough, and the deformation angle at the interface corner edge is smallest. The usefulness of the method is discussed focusing on the deformation angle at the interface corner edge.

A Numerical Method for Solving Matrix Coefficient Heat Equations with Interfaces

AbstractIn this paper, we propose a numerical method for solving the heat equations with interfaces. This method uses the non-traditional finite element method together with finite difference method to get solutions with second-order accuracy. It is capable of dealing with matrix coefficient involving time, and the interfaces under consideration are sharp-edged interfaces instead of smooth interfaces. Modified Euler Method is employed to ensure the accuracy in time. More than 1.5th order accuracy is observed for solution with singularity (second derivative blows up) on the sharp-edged interface corner. Extensive numerical experiments illustrate the feasibility of the method.

Stress Analysis in Polymeric Coating Layer Deposited on Rigid Substrate

This paper presents an analysis of thermal stress induced along the interface between a polymeric coating layer and a steel substrate as a result of uniform temperature change. The epoxy layer is assumed to be a linear viscoelastic material and to be theromorheologically simple. The viscoelastic boundary element method is employed to investigate the behavior of interface stresses. The numerical results exhibit relaxation of interface stresses and large stress gradients, which are observed in the vicinity of the free surface. Since the exceedingly large stresses cannot be borne by the polymeric coating layer, local cracking or delamination can occur at the interface corner.

Debonding strength evaluation in terms of the intensity of singular stress at the interface corner with and without fictitious crack

In this study the debonding strength of adhesively bonded joints is investigated in terms of the intensities of the singular stress fields at the ends of the joints. First, a homogeneous and flawless elastic adhesive layer is assumed to evaluate the butt joint strength for carbon steel/epoxy resin, aluminum/araldite, and brass/solder. It is found that the adhesive strength is always expressed as the critical intensities of singular stress. Next, a small fictitious interface edge crack is assumed at the adhesive layer considering double singular stress fields including and excluding the crack. Then the debonding strength is also found to be controlled by the critical interface stress intensity factor of the fictitious crack. A suitable dimension of the fictitious crack is discussed to predict the strength for adhesive joints accurately and conveniently.

Finite element analysis of lithiation-induced decohesion of a silicon thin film adhesively bonded to a rigid substrate under potentiostatic operation

Insertion-induced stress and interfacial decohesion are studied for a silicon thin film adhesively bonded to a rigid substrate under potentiostatic operation. An axisymmetric finite element model with traction–separation law governing the interfacial degradation is used to study the highly nonlinear diffusion-induced volumetric expansion. Plastic yielding of the film, coupling effects between diffusion and stress, diffusion from both the edge and the top surfaces, and concentration dependence of material properties are considered. It is found interface fails in shear mode, and interfacial decohesion initiates at the interface corner and propagates toward the center. A smaller yield stress of the film is beneficial to structural integrity. The side surface and the top surface near the corner are the critical regions for fracture.

Recursive Algorithms for Distributed Forests of Octrees

The forest-of-octrees approach to parallel adaptive mesh refinement and coarsening has recently been demonstrated in the context of a number of large-scale PDE-based applications. Efficient reference software has been made freely available to the public both in the form of the standalone \tt p4est library and more indirectly by the general-purpose finite element library \tt deal.II, which has been equipped with a \tt p4est backend. Although linear octrees, which store only leaf octants, have an underlying tree structure by definition, it is not fully exploited in previously published mesh-related algorithms. This is because tree branches are not explicitly stored and because the topological relationships in meshes, such as the adjacency between cells, introduce dependencies that do not respect the octree hierarchy. In this work, we combine hierarchical and topological relationships between octants to design efficient recursive algorithms that operate on distributed forests of octrees. We present three important algorithms with recursive implementations. The first is a parallel search for leaves matching any of a set of multiple search criteria, such as leaves that contain points or intersect polytopes. The second is a ghost layer construction algorithm that handles arbitrarily refined octrees that are not covered by previous algorithms, which require a 2:1 condition between neighboring leaves. The third is a universal mesh topology iterator. This iterator visits every cell in a partition, as well as every interface (face, edge, and corner) between these cells. The iterator calculates the local topological information for every interface that it visits, taking into account the nonconforming interfaces that increase the complexity of describing the local topology. To demonstrate the utility of the topology iterator, we use it to compute the numbering and encoding of higher-order $C^0$ nodal basis functions used for finite elements. We analyze the complexity of the new recursive algorithms theoretically and assess their performance, both in terms of single-processor efficiency and in terms of parallel scalability, demonstrating good weak and strong scaling up to 458,000 cores of the JUQUEEN supercomputer.

Cohesive zone finite element analysis of crack initiation from a butt joint’s interface corner

Cohesive zone (CZ) fracture analysis techniques are used to predict the initiation of crack growth from the interface corner of an adhesively bonded butt joint. In this plane strain analysis, a thin linear elastic adhesive layer is sandwiched between rigid adherends. There is no preexisting crack in the problem analyzed, and the focus is on how the shape of the traction–separation (T–U) relationship affects the predicted joint strength. Unlike the case of a preexisting interfacial crack, the calculated results clearly indicate that the predicted joint strength depends on the shape of the T–U relationship. Most of the calculations used a rectangular T–U relationship whose shape (aspect ratio) is defined by two parameters: the interfacial strength σ∗ and the work of separation/unit area Γ. The principal finding of this study is that for a specified adhesive layer thickness, there is any number of σ∗, Γ combinations that generate the same predicted joint strength. Each combination corresponds to a different CZ length. An approximate CZ-like elasticity solution was developed to show how such combinations arise and their connection with the CZ length.