| As the electronics industry continues to push for high performance and miniaturization of electronic devices, the demand for high current density causes electromigration failure in integrated circuits (IC) interconnects and in solder bumps of an IC package. This work reports new findings on the uncertainty that exists in the practice of atomic flux divergence (AFD) method used for studying and quantifying the electromigration (EM) failure of solder joints in wafer level packages. As the name indicates, AFD method calculates the migration of metal atoms. In EM phenomena, the driving forces for mass transportation are current density, temperature gradient, mechanical stress gradient, and atomic density gradient (ADG). But in conventional AFD method (widely used) the effect of ADG is neglected. First, the electromigration phenomenon is studied (using conventional AFD method) in a Lead-free solder joint of an encapsulated copper post wafer level package by finite element modeling. Submodeling method is applied to it. Coupled electrical-, thermal-, and mechanical finite element modeling is performed. Results show the negative values of the divergences of atomic fluxes due to electron current and thermal stresses are obtained under certain loading conditions on cathode side. Such results are contradictory to the published test data. Submodeling presents accurate results if cut boundary is appropriately chosen.;Secondly, current density singularity in electromigration of solder bumps is investigated. A theoretical analysis is performed on a homogenous wedge with arbitrary apex angle, 2(π –&thetas;0), when the current flow passes through. A potential difference is applied at a distance far away from the tip of the wedge. It is found that current density singularity exists at the tip of the wedges when the angles &thetas;0 < 90°. The acute angles represent the corner configuration of the actual solder bump and the interconnect. The current crowding in bumps is a result of singularity exhibited at such corners. Finite element results confirm that the maximum current density has strong dependence on mesh size. To eliminate the singularity effect, a volume-averaged current density approach is suggested.;Finally, another electromigration failure model based on the accumulation of vacancies is studied. This new method is called vacancy concentration method (VCM). In this method vacancy diffusion due to electromigration and migration due to AGD only are considered. A 1-D VCM equation is studied over a conductor stripe simulating a grain boundary. Three reasonable boundary conditions for the electromigration diffusion equation were investigated analytically and numerically. Using a dimensionless parameter, a time to failure for conductors was suggested. It was also seen that if failure was to occur, failure times would follow a j-2 relationship which is in accordance with Black's empirical formula. |
