Fracture mechanics analysis of cracks in solder joint intermetallic compounds

The trend towards miniaturization of electronic products leads to the need for very small sized solder joints. Therefore, there is a higher reliability risk that too large a fraction of solder joints will transform into Intermetallic Compounds (IMCs) at the solder interface. In this paper, fracture mechanics study of the IMC layer for SnPb and Pb-free solder joints was carried out using finite element numerical computer modelling method. It is assumed that only one crack is present in the IMC layer. Linear Elastic Fracture Mechanics (LEFM) approach is used for parametric study of the Stress Intensity Factors (SIF, KI and KII), at the predefined crack in the IMC layer of solder butt joint tensile sample. Contrary to intuition, it is revealed that a thicker IMC layer in fact increases the reliability of solder joint for a cracked IMC. Value of KI and KII are found to decrease with the location of the crack further away from the solder interfaces while other parameters are constant. Solder thickness and strain rate were also found to have a significant influence on the SIF values. It has been found that soft solder matrix generates non-uniform plastic deformation across the solder-IMC interface near the crack tip that is responsible to obtain higher KI and KII.

Birth-death processes with mass annihilation and state-dependent immigration

A birth-death process is subject to mass annihilation at rate β with subsequent mass immigration occurring into state j at rateα j . This structure enables the process to jump from one sector of state space to another one (via state 0) with transition rate independent of population size. First, we highlight the difficulties encountered when using standard techniques to construct both time-dependent and equilibrium probabilities. Then we show how to overcome such analytic difficulties by means of a tool developed in Chen and Renshaw (1990, 1993b); this approach is applicable to many processes whose underlying generator on E\{0} has known probability structure. Here we demonstrate the technique through application to the linear birth-death generator on which is superimposed an annihilation/immigration process.

Time dependent electric, magnetic and hydrodynamic interaction in aluminium electrolysis cells

The waves in commercial cells for electrolytic aluminium production originate at the interface between the liquid aluminium and electrolyte, but their effect can spread into the surrounding busbar network as electric current perturbation, and the total magnetic field acquires a time dependent component. The presented model for the wave development accounts for the nonuniform electric current distribution at the cathode and the whole network of the surrounding busbars. The magnetic field is computed for the continuous current in the fluid zones, all busbars and the ferromagnetic construction elements. When the electric current and the associated magnetic field are computed according to the actual electrical circuit and updated for all times, the instability growth rate is significantly affected. The presented numerical model for the wave and electromagnetic interaction demonstrates how different physical coupling factors are affecting the wave development in the electrolysis cells. These small amplitude self-sustained interface oscillations are damped in the presence of intense turbulent viscosity created by the horizontal circulation velocity field. Additionally, the horizontal circulation vortices create a pressure gradient contributing to the deformation of the interface. Instructive examples for the 500 kA demonstration cell are presented.

Modelling the time-dependent behaviour of solder pastes used in the electronics assembly applications

Solder paste is the most widely used bonding material in the assembly of surface mount devices in electronic industries. It generally has a flocculated structure (show aggregation of solder particles), and hence are known to exhibit a thixotropic behavior. This is recognized by the decrease in apparent viscosity of paste material with time when subjected to a constant shear rate. The proper characterisation of this timedependent rheological behaviour of solder pastes is crucial for establishing the relationships between the pastes’ structure and flow behaviour; and for correlating the physical parameters with paste printing performance. In this paper, we present a novel method which has been developed for characterising the timedependent and non-Newtonian rheological behaviour of solder pastes as a function of shear rates. The objective of the study reported in this paper is to investigate the thixotropic build-up behaviour of solder pastes. The stretched exponential model(SEM) has been used to model the structural changes during the build-up process and to correlate model parameters with the paste printing process.

The ecology of Bacillus thuringiensis on the Phylloplane: colonization from soil, plasmid transfer, and interaction with larvae of Pieris brassicae

Seedlings of clover (Triflorium hybridum) were colonized by Bacillus thuringiensis when spores and seeds were co-inoculated into soil. Both a strain isolated in the vegetative form from the phylloplane of clover, 2810-S-4, and a laboratory strain, HD-1, were able to colonize clover to a density of about 1000 CFU/g leaf when seeds were sown in sterile soil and to a density of about 300 CFU/g leaf in nonsterile soil. A strain lacking the characteristic insecticidal crystal proteins produced a similar level of colonization over a 5-week period as the wild type strain, indicating that crystal production was not a mitigating factor during colonization. A small plasmid, pBC16, was transferred between strains of B. thuringiensis when donor and recipient strains were sprayed in vegetative form onto leaves of clover and pak choi (Brassica campestris var. chinensis). The rate of transfer was about 0.1 transconjugants/recipient and was dependent on the plant species. The levels of B. thuringiensis that naturally colonized leaves of pak choi produced negligible levels of mortality in third instar larvae of Pieris brassicae feeding on the plants. Considerable multiplication occurred in the excreted frass but not in the guts of living insects. Spores in the frass could be a source of recolonization from the soil and be transferred to other plants. These findings illustrate a possible cycle, not dependent on insect pathology, by which B. thuringiensis diversifies and maintains itself in nature.

Modelling of the time-dependent flow behaviour of lead-free solder pastes used for flip-chip assembly applications

The market for solder paste materials in the electronic manufacturing and assembly sector is very large and consists of material and equipment suppliers and end users. These materials are used to bond electronic components (such as flip-chip, CSP and BGA) to printed circuit boards (PCB's) across a range of dimensions where the solder interconnects can be in the order of 0.05mm to 5mm in size. The non-Newtonian flow properties exhibited by solder pastes during its manufacture and printing/deposition phases have been of practical concern to surface mount engineers and researchers for many years. The printing of paste materials through very small-sized stencil apertures is known to lead to increased stencil clogging and incomplete transfer of paste to the substrate pads. At these very narrow aperture sizes the paste rheology and particle-wall interactions become crucial for consistent paste withdrawal. These non-Newtonian effects must be understood so that the new paste formulations can be optimised for consistent printing. The focus of the study reported in this paper is the characterisation of the rheological properties of solder pastes and flux mediums, and the evaluation of the effect of these properties on the pastes' printing performance at the flip-chip assembly application level. Solder pastes are known to exhibit a thixotropic behaviour, which is recognised by the decrease in apparent viscosity of paste material with time when subjected to a constant shear rate. The proper characterisation of this time-dependent theological behaviour of solder pastes is crucial for establishing the relationships between the pastes' structure and flow behaviour; and for correlating the physical parameters with paste printing performance. In this paper, we present a number of methods which have been developed for characterising the time-dependent and non-Newtonian rheological behaviour of solder pastes and flux mediums as a function of shear rates. We also present results of the study of the rheology of the solder pastes and flux mediums using the structural kinetic modelling approach, which postulates that the network structure of solder pastes breaks down irreversibly under shear, leading to time and shear dependent changes in the flow properties. Our results show that for the solder pastes used in the study, the rate and extent of thixotropy was generally found to increase with increasing shear rate. The technique demonstrated in this study has wide utility for R&D personnel involved in new paste formulation, for implementing quality control procedures used in solder paste manufacture and packaging; and for qualifying new flip-chip assembly lines