Influence of temperature gradient on electromigration failures in 3D packaging

In this paper, influence of temperature gradient in interconnects due to Joule heating in 3D packaging on electromigration failure is presented. Black's Mean Time to Failure (MTF) model relates exponentially to the temperature of interconnects which is assumed to be constant hence does not take into account temperature gradient. The developed electromigration model incorporates the driving force due to temperature gradient in addition to the effects of current density, vacancy concentration gradients and stress gradients in the interconnects and due to coefficient of thermal expansion mismatch with surrounding materials. Effectiveness of the developed finite element model is illustrated complex C4 solder bumps of flip-chip packages using COMSOL Mutliphysics software. It is shown that for same current density in the complex C4 solder bumps of flip-chip packages it is possible that failure times could be lower for lower solder average temperature with higher temperature gradient than for higher solder temperature with low temperature gradient.