High electric current density-induced interfacial reactions in micro ball grid array (μBGA) solder joints

The effect of a high electric current density on the interfacial reactions of micro ball grid array solder joints was studied at room temperature and at 150 °C. Four types of phenomena were reported. Along with electromigration-induced interfacial intermetallic compound (IMC) formation, dissolution at the Cu under bump metallization (UBM)/bond pad was also noticed. With a detailed investigation, it was found that the narrow and thin metallization at the component side produced “Joule heating” due to its higher resistance, which in turn was responsible for the rapid dissolution of the Cu UBM/bond pad near to the Cu trace. During an “electromigration test” of a solder joint, the heat generation due to Joule heating and the heat dissipation from the package should be considered carefully. When the heat dissipation fails to compete with the Joule heating, the solder joint melts and molten solder accelerates the interfacial reactions in the solder joint. The presence of a liquid phase was demonstrated from microstructural evidence of solder joints after different current stressing (ranging from 0.3 to 2 A) as well as an in situ observation. Electromigration-induced liquid state diffusion of Cu was found to be responsible for the higher growth rate of the IMC on the anode side.

Policy-centric integration and dynamic composition of autonomic computing techniques

This paper presents innovative work in the development of policy-based autonomic computing. The core of the work is a powerful and flexible policy-expression language AGILE, which facilitates run-time adaptable policy configuration of autonomic systems. AGILE also serves as an integrating platform for other self-management technologies including signal processing, automated trend analysis and utility functions. Each of these technologies has specific advantages and applicability to different types of dynamic adaptation. The AGILE platform enables seamless interoperability of the different technologies to each perform various aspects of self-management within a single application. The various technologies are implemented as object components. Self-management behaviour is specified using the policy language semantics to bind the various components together as required. Since the policy semantics support run-time re-configuration, the self-management architecture is dynamically composable. Additional benefits include the standardisation of the application programmer interface, terminology and semantics, and only a single point of embedding is required.

Numerical simulation of flow-induced cavity noise in self-sustained oscillations

The generation and near-field radiation of aerodynamic sound from a low-speed unsteady flow over a two-dimensional automobile door cavity is simulated by using a source-extraction-based coupling method. In the coupling procedure, the unsteady cavity flow field is first computed solving the Reynolds averaged Navier–Stokes (RANS) equations. The radiated sound is then calculated by using a set of acoustic perturbation equations with acoustic source terms which are extracted from the time-dependent solutions of the unsteady flow. The aerodynamic and its resulting acoustic field are computed for the Reynolds number of 53,266 based on the base length of the cavity. The free stream flow velocity is taken to be 50.9m/s. As first stage of the numerical investigation of flow-induced cavity noise, laminar flow is assumed. The CFD solver is based on a cell-centered finite volume method. A dispersion-relation-preserving (DRP), optimized, fourth-order finite difference scheme with fully staggered-grid implementation is used in the acoustic solver

Multiple reflow study of ball grid array (BGA) solder joints on Au/Ni metallization

This paper evaluates the shearing behavior of ball grid array (BGA) solder joints on Au/Ni/Cu pads of FR4 substrates after multiple reflow soldering. A new Pb-free solder, Sn–3Ag–0.5Cu–8In (SACI), has been compared with Sn–3Ag–0.5Cu (SAC) and Sn–37Pb (SP) solders, in terms of fracture surfaces, shearing forces and microstructures. Three failure modes, ball cut, a combination of solder shear and solder/pad bond separation, and pad lift, are assessed for the different solders and reflow cycles. It is found that the shearing forces of the SP and SAC solder joints tend to increase slightly with an increase in the number of reflow cycles due to diffusion-induced solid solution strengthening of the bulk solder and augmentation of the shearing area. However, the shearing forces of the SACI solder joints decrease slightly after four cycles of reflow, which is ascribed to the thermal degradation of both the solder/intermetallic compound (IMC) and IMC/Ni interfaces. The SACI solder joints yield the highest strengths, whereas the SP solder joints give the smallest values, irrespective of the number of reflow cycles. Thickening of the interfacial IMC layer and coarsening of the dispersing IMC particles within the bulk solders were also observed. Nevertheless, the variation of shearing forces and IMC thickness with different numbers of reflow cycles was not so significant since the Ni under layer acted as an effective diffusion barrier. In addition, the initially-formed IMC layer retarded the further extensive dissolution of the pad material and its interaction with the solder

Shear strength analysis of ball grid array (BGA) solder interfaces

Ball shear test is the most common test method used to assess the reliability of bond strength for ball grid array (BGA) packages. In this work, a combined experimental and numerical study was carried out to realize of BGA solder interface strength. Solder mask defined bond pads on the BGA substrate were used for BGA ball bonding. Different bond pad metallizations and solder alloys were used. Solid state aging at 150degC up to 1000 h has been carried out to change the interfacial microstructure. Cross-sectional studies of the solder-to-bond pad interfaces was conducted by scanning electron microscopy (SEM) equipped with an energy dispersive X-ray (EDX) analyzer to investigate the interfacial reaction phenomena. Ball shear tests have been carried out to obtain the mechanical strength of the solder joints and to correlate shear behaviour with the interfacial reaction products. An attempt has been taken to realize experimental findings by Finite Element Analysis (FEA). It was found that intermetallic compound (IMC) formation at the solder interface plays an important role in the BGA solder bond strength. By changing the morphology and the microchemistry of IMCs, the fracture propagation path could be changed and hence, reliability could be improved

An algorithm for total variation inpainting based on nonlinear multi-grid methods

Image inpainting refers to restoring a damaged image with missing information. The total variation (TV) inpainting model is one such method that simultaneously fills in the regions with available information from their surroundings and eliminates noises. The method works well with small narrow inpainting domains. However there remains an urgent need to develop fast iterative solvers, as the underlying problem sizes are large. In addition one needs to tackle the imbalance of results between inpainting and denoising. When the inpainting regions are thick and large, the procedure of inpainting works quite slowly and usually requires a significant number of iterations and leads inevitably to oversmoothing in the outside of the inpainting domain. To overcome these difficulties, we propose a solution for TV inpainting method based on the nonlinear multi-grid algorithm.

Numerical solutions of certain nonlinear models in European options on a distributed computing environment

Financial modelling in the area of option pricing involves the understanding of the correlations between asset and movements of buy/sell in order to reduce risk in investment. Such activities depend on financial analysis tools being available to the trader with which he can make rapid and systematic evaluation of buy/sell contracts. In turn, analysis tools rely on fast numerical algorithms for the solution of financial mathematical models. There are many different financial activities apart from shares buy/sell activities. The main aim of this chapter is to discuss a distributed algorithm for the numerical solution of a European option. Both linear and non-linear cases are considered. The algorithm is based on the concept of the Laplace transform and its numerical inverse. The scalability of the algorithm is examined. Numerical tests are used to demonstrate the effectiveness of the algorithm for financial analysis. Time dependent functions for volatility and interest rates are also discussed. Applications of the algorithm to non-linear Black-Scholes equation where the volatility and the interest rate are functions of the option value are included. Some qualitative results of the convergence behaviour of the algorithm is examined. This chapter also examines the various computational issues of the Laplace transformation method in terms of distributed computing. The idea of using a two-level temporal mesh in order to achieve distributed computation along the temporal axis is introduced. Finally, the chapter ends with some conclusions.

Grid effects

Zaha Hadid's Kartal Pendik Masterplan (2006) for a new city centre on the east bank of Istanbul proposes the redevelopment of an abandoned industrial site located in a crucial infrastructural node between Europe and Asia as a connecting system between the neighbouring areas of Kartal in the west and Pendik in the east. The project is organised on what its architects call a soft grid, a flexible and adaptable grid that allows it to articulate connections and differences of form, density and use within the same spatial structure [1]. Its final overall design constitutes only one of the many possible configurations that the project may take in response to the demands of the different areas included in the masterplan, and is produced from a script that is able to generate both built volumes and open spaces, skyscrapers as well as parks. The soft grid in fact produces a ‘becoming’ rather than a finite and definitive form: its surface space does not look like a grid, but is derived from a grid operation which is best explained by the project presentation in video animation. The grid here is a process of ‘gridding’, enacted according to ancient choreographed linear movements of measuring, defining, adjusting, reconnecting spaces through an articulated surface rather than superimposed on an ignored given like an indifferent colonising carpet.