Grain boundary grooving and cathode voiding in bamboo-like metallic interconnects by surface drift diffusion under the capillary and electromigration forces

摘要

The process of grain boundary (GB) grooving and cathode voiding in sandwich type thin film bamboo lines are 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 is followed by the familiar time law as t~(1/4), at the steady state regime. The applied electric field (EF) in constant current experiments modifies this time law drastically above the well-defined electron wind intensity (EWI) threshold, and puts an upper limit for the groove depth, which decreases monotonically with EWI. Below the threshold level, the capillary regime predominates, and EF has little effect on the general kinetics of GB grooving, other than the linear increase in total elapsed time with EWI. An analytical formula for the cathode failure time in constant voltage test is obtained in terms of the system parameters, which are closely associated with the cathode voiding or grain thinning by surface drift diffusion.