Growth of single crystals under magnetic field is of interest for suppressing the adverse effect of natural convection and for better mixing in the liquid solution, which are the favorable conditions for prolonged growth and high quality crystals. In this short review article, recent developments in the modelling of electroepitaxy under magnetic field are presented. An application is given for the liquid phase electroepitaxial growth of GaAs bulk single crystals under a static magnetic field. Experimental results, that have shown that the growth rate under an applied static magnetic field is proportional to the applied magnetic field, and increases with the field intensity level, are predicted from the present model. The model also predicts growth interface shapes accurately.
The bump resistance of flip-chip solder joints was measured experimentally and analyzed by the finite-element method. Kelvin structures for flip-chip solder joints were designed and fabricated to measure the bump resistance. The measured value was only about 0.9 mV at room temperature, which was much lower than that expected. Three-dimensional (3-D) modeling was performed to examine the current and voltage distribution in the joint. The simulated value was 7.7 mV, which was about 9 times larger than the experimental value. The current crowding effect was found to be responsible for the difference in bump resistance. Therefore, the measured bump resistance strongly depended on the layout of the Kelvin structure. Various layouts were simulated to investigate the geometrical effect of bump resistance, and a significant geometrical effect was found. A proper layout was proposed to measure the bump resistance correctly. The Kelvin structure would play an important role in monitoring void formation and microstructure changes during the electromigration of flip-chip solder joints.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.