6 resultados para stream function-vorticity-current density

em Greenwich Academic Literature Archive - UK


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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.

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High current density induced damages such as electromigration in the on-chip interconnection /metallization of Al or Cu has been the subject of intense study over the last 40 years. Recently, because of the increasing trend of miniaturization of the electronic packaging that encloses the chip, electromigration as well as other high current density induced damages are becoming a growing concern for off-chip interconnection where low melting point solder joints are commonly used. Before long, a huge number of publications have been explored on the electromigration issue of solder joints. However, a wide spectrum of findings might confuse electronic companies/designers. Thus, a review of the high current induced damages in solder joints is timely right this moment. We have selected 6 major phenomena to review in this paper. They are (i) electromigration (mass transfer due electron bombardment), (ii) thermomigration (mass transfer due to thermal gradient), (iii) enhanced intermetallic compound growth, (iv) enhanced current crowding, (v) enhanced under bump metallisation dissolution and (vi) high Joule heating and (vii) solder melting. the damage mechanisms under high current stressing in the tiny solder joint, mentioned in the review article, are significant roadblocks to further miniaturization of electronics. Without through understanding of these failure mechanisms by experiments coupled with mathematical modeling work, further miniaturization in electronics will be jeopardized

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An electrolytic cell for Aluminum production contains molten metal subject to high currents and magnetic flux density. The interaction between these two fields creates electromagnetic forces within the liquid metal and can generate oscillations of the fluid similar to the waves at the free surface of oceans and rivers. The study of this phenomenon requires the simulation of the current density field, of the magnetic flux density field and the solution of the equations of motion of the liquid mass. An attempt to analyze the dynamical behavior of this problem is made by coupling different codes, based on different numerical techniques, in a single tool. The simulations are presented and discussed.

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The main goal of a cell stability MHD model like MHD-Valdis is to help locate the busbars around the cell in a way which leads to the generation of a magnetic field inside the cell that itself leads to a stable cell operation. Yet as far as the cell stability is concerned, the uniformity of the current density in the metal pad is also extremely important and can only be achieved with a correct busbar network sizing. This work compares the usage of a detailed ANSYS based 3D thermo-electric model with the one of the versatile 1D part of MHD-Valdis to help design a well balanced busbar network.

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The MHD wave instability in commercial cells for electrolytic aluminium production is often described using ‘shallow water’ models. The model [1] is extended for a variable height cathode bottom and anode top to account for realistic cell features. The variable depth of the two fluid layers affects the horizontal current density, the wave development and the stability threshold. Instructive examples for the 500 kA cell are presented.

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The effects of a constant uniform magnetic field on a growing equiaxed crystal are investigated using a 3-dimensional enthalpy based numerical model. Two cases are considered: The first case looks at unconstrained growth, where the current density is generated through the thermo-electric effect and the current circulates between the tips and roots of the dendrite, the second represents an imposed potential difference across the domain. A jump in the electrical conductivity between the liquid and solid causes the current density to be non uniform. In both cases the resulting Lorentz force drives fluid flow in the liquid phase, this in turn causes advection of the thermal and solute field altering the free energy close to the interface and changing the morphology of the dendrite. In the first case the flow field is complex comprising of many circulations, the morphological changes are modelled using a 2D model with a quasi 3D approximation. The second case is comparable to classic problems involving a constant velocity boundary.