A Study on the Mechanism of Crystal Cracking in GTA Welding of Copper Plates

Crystal cracking is one of the major defects when large copper structures are joined by gas tungsten arc welding (GTA welding). In order to research the mechanism of crystal cracking, the criterion for crystal cracking formation has been optimized based on Prokhorov's theory, which shows that the interior deformation rate (Δ?) is the main factor that leads to crystal cracking. A finite element model of thick copper plates in GTA welding based on the rigid constraint experiments has been established, and the Δ? variation of the welds is obtained. The physical model of the tendency of crystal cracking has been established, and then the mechanism of crystal cracking has been discussed systematically by comparing the variations between Δ? obtained from numerical simulations and the weld ductility (P_min) obtained from hot-tension experiments within the brittle temperature range (BTR). Results show that during GTA welding, the values of Δ? and P_min are varied, respectively, with the temperature descending, and the tendency of crystal cracking and expansion velocity can be controlled by the value of (Δ? ? P_min). Then experiments with the preheated temperatures of 300°C and 500°C, verified the validity of the optimized criterion of cracking.     

High aspect ratio via etch development for Cu nails in 3-D-stacked ICs

In this study the etch development of high aspect ratio vias in Si for the fabrication of Cu nails is described. To enable subsequent metallisation, these vias need to meet strict requirements with respect to uniformity, slope, sidewall roughness and undercut. For aspect ratios up to 5 a SiO₂ hard mask based SF6/O₂ etch approach is used. For aspect ratios up to 10, a resist based passivation polymer type etch approach with C4F8/SF6 was used to successfully pattern vias in Si. Typical problems of this process and optimization to overcome the issues are described.     

Nd:YAG laser drilling in epoxy resin/AlN composites material

The Nd:YAG laser drilling performance of blind vias in epoxy/aluminium nitride (AlN) composite and virgin epoxy is systemically studied through varying the average laser power, the repetition times, and the pulse repetition rate from 0.2 W to 1.2 W, 12 to 48 and 3 KHz to 20 KHz, respectively. The results show that compared with pure epoxy, the drilling conditions of blind vias in epoxy/AlN composite can be changed in a wide range, with no residue found significantly at the surface of the entrance of the blind vias. The influence of the repetition rate is more evident among the parameters of the Nd:YAG laser, such as the average laser power, laser repetition rate, and repetition times, and should be carefully controlled.     

A New Quantum Formalism for Damping and Gain in Harmonic Oscillators

Abstract

A new formulation of loss or gain in the quantum theory of harmonic oscillators is put forward using a non-passive reactive circuit which can be readily quantized. The analysis is based on the electrical circuit theory and demonstrates how a circuit, with negative inductance ? L _n and negative capacitance ? C _n, coupled to a conventional harmonic oscillator circuit, of positive inductance L and positive capacitance C, can act as a source or sink of energy and allow for both gain and loss. Classically this series circuit is indistinguishable in its transients from either a + G or ? G conductance shunted across a main LC oscillator circuit. However, unlike the resistive circuit, this coupled circuit can be quantized, maintaining the uncertainty principle. A two-valued solution is found, dependent on whether the circuits are in a state to receive energy or a state to absorb energy. A full correspondence, including second-order frequency shifts, is found between the quantum and the classical solutions with states which are appropriate to thermodynamic equilibrium of a conductance at a temperature T as well as to the classical-like coherent states. While the accessible mode in the + L + C circuit does not exhibit any squeezing directly, the system as a whole is an example of two-mode squeezing discussed by other authors.     

Modelling of transverse crack growth and saturation in cross-ply laminates

A model of transverse cracking in cross-ply laminates is presented. The model describes the onset of cracking, the development of the number of cracks, the saturation phase of this damage mode and the final crack distribution, as well as the dependency of these phenomena on the 90° ply thickness. This analysis is based on an effective flaw size distribution and a non-linear interlaminar behaviour hypothesis. The theoretical prediction of the process and the saturation of cracking was well correlated with the experiments conducted on [O₂/90 _n ]_s graphite/epoxy. However, there was considerable dispersion in the experimental results concerning the onset of cracking. Experimental work and part of the theoretical investigations were made at ONERA, 29 av. Division, Leclerc 92322, Chatillan, Cedex, France.     

Crack-Tip Stress-Strain Fields During Cyclic Loading and Effect of Overload

Finite-deformation elastoplastic analysis of a plane-strain crack subjected to mode I cyclic loading under small scale yielding was performed. The influence of the load range, load ratio and overload on the crack tip stress-strain field is presented. Two independent parameters of cyclic loading, such as ΔK and K _max, both substantially affect the near tip evolutions of cyclic stresses and plastic strains, in agreement with typical experimental trends of fatigue cracking. This implies that the behaviour of cracks is governed by stress and strain fields ahead of the tip, via their control over the key process variables (damage accumulation and rupture, i.e., bond-breaking), so that the coupled process becomes a two-parameter one in terms of fracture mechanics variables ΔK and K _max.     

Electromigration Failure of Metal Lines

With the scaling down process of microcircuits in semiconductor devices, the density of electric current in interconnecting metal lines increases, and the temperature of the device itself rises. Electromigration is a phenomenon that metallic atoms constructing the line are transported by electron wind. The damage induced by electromigration appears as the formation of voids and hillocks. The growth of voids in the metal lines ultimately results in electrical discontinuity. Our research group has attempted to identify a governing parameter for electromigration damage in metal lines, in order to clarify the electromigration failure and to contribute to circuit design. The governing parameter is formulated based on the divergence of the atomic flux by electromigration, and is denoted by AFD. The prediction method for the electromigration failure has been developed by using AFD. The AFD-based method makes it possible to predict the lifetime and failure site in universal and accurate way. In the actual devices, the metal lines used in the integrated circuit products are covered with a passivation layer, and the ends of the line are connected with large pads or vias for current input and output. Also, the microstructure of metal line distinguishes the so-called bamboo structured line from polycrystalline line depending on the size of metallic grains relative to the line width. Considering the damage mechanisms depending on such line structure, our research group has made a series of studies on the development of the prediction method. This article is dedicated to make a survey of some recent achievements for realizing a reliable circuit design against electromigration failure.     

EFSIM: An integrated circuit early failure simulator

Early failures are the dominant concern as integrated circuit technology matures into consistently producing systems of high reliability. These failures are attributed to the presence of randomly occurring defects in elementary objects (contacts, vias, metal runs, gate oxides, bonds etc.) that result in extrinsic rather than intrinsic (wearout-related) mortality. A model relating system failure to failure at the elementary object level has been developed. Reliability is modelled as a function of circuit architecture, mask layout, material properties, life-test data, worst-case use-conditions and the processing environment. The effects of competing failure mechanisms, and the presence of redundant sub-systems are accounted for. Hierarchy is exploited in the analysis, allowing large scale designs to be simulated. Experimental validation of the modelling of oxide leakage related failure, based on a correlation between actual failures reported for a production integrated circuit and Monte Carlo simulations that incorporate wafer-level test results and process defect monitor data, is presented. The state of the art in IC reliability simulation is advanced in that a methodology that provides the capability to design-in reliability while accounting for early failures has been developed; applications include process qualification, design assessment and fabrication monitoring.     

基于全量流动理论的管材弯曲过程失稳分析研究

目的 基于全量流动理论,研究管材弯曲成形过程中的外侧破裂和内侧起皱,分析其产生的原因及控制方法.方法 采用理论解析方法,建立了管材弯曲变形应力、应变计算公式,推导管材外侧破裂和内侧起皱发生的判据,并试验验证了预测公式的可靠性.结果 基于推导的应力、应变计算公式,依据临界许用变形程度,建立了管材外侧破裂判据;采用能量准则...     

Confidence bounds for the reliability of binary capacitated two-terminal networks

Binary capacitated two-terminal reliability at demand level d (2TR_d) is defined as the probability that network capacity, generated by binary capacitated components, between specified source and sink nodes is greater than or equal to a demand of d units. For the components that comprise these networks, reliability estimates are usually obtained from some source of testing. For these estimates and depending on the type of testing, there is an associated uncertainty that can significantly affect the overall estimation of 2TR_d. That is, an accurate estimate of 2TR_d is highly dependent on the uncertainty associated to the reliability of the network components. Current methods for the estimation of network reliability and associated uncertainty are restricted to the case where the network follows a series-parallel architecture and the components are binary and non-capacitated. For different capacitated network designs, an estimate on 2TR_d can only be approximated for specific scenarios. This paper presents a bounding approach for 2TR_d by explaining how component reliability and associated uncertainty impact estimates at the network level. The proposed method is based on a structured approach that generates a α-level confidence interval (CI) for binary capacitated two-terminal network reliability. Simulation results on different test networks show that the proposed methods can be used to develop very accurate bounds of two-terminal network reliability.     

Direct Observation of Fatigue Cracking in the Fuel Plate Using the Scanning Electron Microscope

Safety and environmental considerations play the important role in selecting and processing fusion materials. Fatigue impairs the reliability of the components utilized in the fusion reactor. In this paper, we described the fatigue cracking mechanism of the sandwich structure of dispersion U₃Si₂-Al fuel plates using the in situ scanning electron microscope. Direct observations indicated that the failure originates in the vicinal clad-meat interface under tensile-tensile cyclic and three points bending loading. The fatigue crack occurs in two typical fracture modes — Mode-I and the mixed-mode of I and II. The effect of the process of U₃Si₂-Al fuel meat on the fatigue behaviors of the sandwich structure is obvious.     

Reliability study of through-silicon via (TSV) copper filled interconnects

Through-silicon vias (TSVs) have been extensively studied because of their ability to achieve chip stacking for enhanced system performance. The fabrication process is becoming somewhat mature. However, reliability issues need to be addressed in order for an eventual transition from laboratory to production. In our laboratory, vias with tapered sidewalls are formed through a modified Bosch process using deep reactive ion etching (DRIE). Vias are lined with silicon dioxide using plasma enhanced chemical vapor deposition (PECVD) followed by sputter deposited titanium barrier and copper seed layers before filling with a reverse pulse copper electroplating process. Following attachment of the process wafer to a carrier wafer, the process wafer is thinned from the backside by a combination of mechanical methods and reactive ion etching (RIE). Fabricated vias are subjected to thermal cycling with temperatures ranging from − 25 °C to 125 °C. For via chains, erratic changes in resistance upon temperature cycling indicated a problem with the wire bonds used to connect the sample to the test fixture. Test methods were modified to avoid wire bonding and form the basis of reliability studies presented in this paper. TSVs are shown to be stable with small increases in measured resistance for 200 cycles. In addition, small changes in resistance are observed when vias are held at elevated temperatures for extended periods of time.     

Deformation behavior of complex carbon nitride and metal nitride based bi-layer coatings

A bi-layer coating consisting of a TiAlCrN inner layer and complex carbon nitride (CN_x) plus CrCN outer layer was deposited on to a high speed steel (M2) substrate via physical vapour deposition (PVD). Detailed microstructural analysis of the coating has been performed via transmission electron microscopy (TEM) and X-ray photoelectron spectroscopy (XPS). XPS analysis indicated that the outer layer contained both C-C bonds, associated with an amorphous phase, and the presence of CrCN, which was confirmed by TEM analysis. Localized deformation of the coating was performed using nanoindentation with a spherical indenter. Force-displacement curves of the indentation tests exhibited a number of ‘pop-ins’ during the loading cycle, indicative of cracking and other deformation events. Cross-sectional analysis of the indents revealed extensive cracking in the TiAlCrN layer and shear steps at the steel-nitride interface, consistent with the events observed in the force-displacement curves. On the other hand minimal cracking was observed in the CN_x + CrCN layer. It is believed that the relatively ductile outer layer inhibits the propagation of cracks from the inner, brittle layer.     

吸湿对印制电路板层压板热膨胀系数的影响

水分对印制电路板的可靠性有重要影响.电路板中的水分子可以改变电路基板的热性能及热力学性能,从而影响电路板及元器件的正常功能.研究了吸湿对两种无卤PCB及两种含卤PCB层压板热膨胀系数的影响,评价了IPC-TM-650 2.4.24测试方法中预处理方法对吸湿样品的适用性.结果表明,PCB层压板中的水分对PCB层压板的热膨胀曲线有明显影响,但传统的热膨胀系数计算方法并不能显示这种影响,对此作了详细分析并提出了改进建议.同时,IPC测试方法中的预处理可以降低湿度对样品热膨胀曲线的影响,但不能完全消除.     

Estimation of the Stress-Strength Reliability for Exponentiated Pareto Distribution Using Median and Ranked Set Sampling Methods

In reliability analysis, the stress-strength model is often used to describe the life of a component which has a random strength (X) and is subjected to a random stress (Y). In this paper, we considered the problem of estimating the reliability R=P [Y<X] when the distributions of both stress and strength are independent and follow exponentiated Pareto distribution. The maximum likelihood estimator of the stress strength reliability is calculated under simple random sample, ranked set sampling and median ranked set sampling methods. Four different reliability estimators under median ranked set sampling are derived. Two estimators are obtained when both strength and stress have an odd or an even set size. The two other estimators are obtained when the strength has an odd size and the stress has an even set size and vice versa. The performances of the suggested estimators are compared with their competitors under simple random sample via a simulation study. The simulation study revealed that the stress strength reliability estimates based on ranked set sampling and median ranked set sampling are more efficient than their competitors via simple random sample. In general, the stress strength reliability estimates based on median ranked set sampling are smaller than the corresponding estimates under ranked set sampling and simple random sample methods.     

A survey of failure criteria and parameters in mixed-mode fatigue crack growth

From the present survey of the mixed-mode crack growth criteria based on the fracture toughness K _Ic (critical J-integral), it follows that this concept is very extensively and variously used by different authors. The criteria discussed in the work are based on the parameters K, δ, W, and J. The most extensively applied models include the mixed mode I + II described by the stress intensity factor K. The criteria presented in the work are based on the factors affecting the fatigue crack growth during testing, namely stress, crack-tip displacement, or energy dissipation. In the case of mixed-mode cracking, special attention should be paid to the energy approach (application of the J-integral and strain energy density), which seems to be very promising for elastoplastic materials. Under mixed-mode cracking, two things should be taken into account: the rate and direction of fatigue-crack growth. Moreover, the nonproportional loading, crack closure, or overloads strongly affect the process of fatigue crack growth in the case of mixed-mode cracking.     

Vickers Indentation Fracture (VIF) modeling to analyze multi-cracking toughness of titania, alumina and zirconia plasma sprayed coatings

For massive brittle materials, the fracture toughness in mode I, K_IC, can be determined using various reliable techniques. Besides, Vickers Indentation Fracture (VIF) technique has been developed to locally determine fracture toughness. However, since the indentation test generates a complex three-dimensional crack system around the indent, fracture toughness, K_C, is calculated instead of K_IC. Consequently some authors rightly reject the VIF technique to determine standard fracture toughness by arguing that the literature counts numerous VIF crack equations thus revealing discrepancies of this technique. Nevertheless in some cases (e.g. brittle ceramic coatings) inclusive material techniques are not applicable since presence of the substrate and/or multi-crack network can modify the crack propagation into the coating.In this work, we employed VIF technique to study multi-cracking behavior of titania, alumina and zirconia ceramic oxide coatings obtained by plasma spraying. To calculate VIF toughness, we propose (i) to select two crack equations for radial-median and Palmqvist cracking modes respectively, (ii) to adjust the crack equation of Miranzo and Moya for intermediate cracking mode, (iii) to develop a mathematical approach to determine the cracking mode, (iv) to take into account the multi-crack network by defining an equivalent four-crack system and (v) to propose a universal crack equation applicable independently of the cracking mode.     

Correlation between resin material variables and transverse cracking in composites

In this paper, the correlation between the resin material variables and the transverse cracking in composites is established. A theoretical model based on the fracture mechanics principle is built to describe thein situ failure process of transverse cracking. The central concept of the model is that the fracture is controlled by the plastic zone developed at the crack tip. Based on an approximate crack tip stress distribution, a quantitative representation is found to relate the laminate transverse cracking fracture toughness,G _c(comp), to certain resin properties: fracture toughness,G _c(resin), yield stress, _y, Young's modulus,E, and residual stress build-up, _R.G _c(comp) values of several fibre-glass/epoxy laminate systems were measured using the double torsion technique. The experimental results are found to be interpreted reasonably well by the theory. As a result, a clear picture of transverse cracking emerges. It seems that _y ²/E plays a more dominant role thanG _c(resin) in controllingG _c(comp). The residual stress _R can weaken the laminate significantly when its level is high. It is also shown that the failure model discussed here can be readily applied to laminate delamination failure as well as adhesive bond fracture.     

Hydrogen assisted intergranular cracking in steels

McMahon suggested that interface decohesion at grain-boundary carbides and precipitates is the mechanism of hydrogen assisted intergranular cracking, HAIC, in high strength steels. In general, cleavage of grain-boundary carbides, adhesion failure or interface decohesion at grain-boundary carbides and precipitates, and crack-tip shear slip along the grain boundary could be the mechanisms of HAIC. Hydrogen reduces cleavage strength, adhesion strength and the resistance to shear slip; therefore, hydrogen assists intergranular cracking. A method of identifying such mechanisms is suggested. A generalized theory of hydrogen assisted cracking is deduced. Brittle crystals cleave on their cleavage planes. Cleavage cracking of such crystals is anisotropic. When the crack-tip stress intensity factor, K, is low, the tortuous cracking process from the anisotropy results in rapidly increasing Stage-I crack growth rate with respect to K. The mechanism of the crack growth threshold, K_TH, is also discussed.     

Analysis and simulation of cracking patterns in coating under biaxial tensile or thermal stress using analysis/FEM strain-accommodation method

The cracking patterns in coatings under biaxial tensile or thermal stress are analyzed by the “analysis/FEM strain-accommodation method” that combines the strain of the substrate with a coating obtained from thermo-elastic analysis with the strain of the substrate calculated by a finite element method. The simulation using this method is effective not only for expressing the cracking patterns observed in punch press tests of disk specimens with WC-Co cermet and Al₂O₃-TiO₂ ceramic coatings but also predicting the cracking process for the coating deposited on a part with a complex shape under thermal stress.