The process of grain boundary grooving and cathode voiding in sandwich type thin film bamboo lines were simulated by introducing a mathematical model, which flows from the fundamental postulates of irreversible thermodynamics. In the absence of the electric field, the computer studies on the triple junction kinetics show that it obeys the first order reaction kinetics at early transient stage, which was followed by the familiar time law as t1/4, at the steady state regime. The applied electric field in constant current experiments modifies this time law drastically above the well-defined electron wind intensity threshold, and puts an upper limit for the groove depth, which decreased monotonically with electron wind intensity. Below the threshold level, the capillary regime predominates, and electric field has little effect on the general kinetics of grain boundary grooving, other than the linear increase in total elapsed time with electron wind intensity. An analytical formula for the cathode failure time in constant voltage test was obtained in terms of the system parameters, which were closely associated with the cathode voiding or grain thinning by surface drift diffusion.

Grain Boundary Grooving and Cathode Voiding in Bamboo-Like Metallic Interconnects by Surface Drift Diffusion under Capillary and Electromigration Forces. T.O.Ogurtani, O.Akyildiz: Journal of Applied Physics, 2005, 97[9], 093520 (9pp)