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

Abstract

The process of grain boundary ͑GB͒ 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 ͑EF͒ in constant current experiments modifies this time law drastically above the well-defined electron wind intensity ͑EWI͒ 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.

Cathode edge displacement by voiding coupled with grain boundary grooving in bamboo like metallic interconnects by surface drift-diffusion under the capillary and electromigration forces

“…The data related to the GB groove peaking times (GPT) for various electron wind intensities is also plotted in Fig. 4, which shows that there is a very close correlation between GPT, where the strange groove tip velocity inversion (healing effect) takes place (Ogurtani and Akyildiz, 2005) and the cathode drift onset time, which may be called as the cathode drift incubation time.…”

“…The main difference comes from the form of the analytical functions that describes the time dependence of the cathode shrinkage processes at the cathode regions, which are given by Eq. (19) of recent work of Ogurtani and Akyildiz (2005) and Eq. (13) of this article, respectively.…”

“…Two different experimental procedures were applied to reveal this peculiar phenomenon. The first procedure as described in the previous article (Ogurtani and Akyildiz, 2005) uses reflecting boundary conditions (R-BC) at both ends of the interconnect specimen, and starts with application of the constant voltage differential to the electrodes up to the point where the almost complete cathode failure (95%) occurs by voiding. Under the constant voltage differential testing, the complete cathode detachment actually never takes place ð t CFT !…”

“…This article primarily focuses on the non-equilibrium thermodynamic treatment of the cathode shrinkage and drift processes coupled with the GB grooving, and carried out Blech-type experimental configuration, under CC as a further supplement for our previous work (Ogurtani and Akyildiz, 2005). In that work the main concern was the study of the morphological surface evolution dynamics associated with GB grooving kinetics coupled with the cathode contact area shrinkage and/or cathode voiding using SOCV operation.…”

Irreversible thermodynamics of triple junctions during the intergranular void motion under the electromigration forces

“…The singular points such as grain boundary grooves, and internal voids trapped by grain boundaries should be analyzed carefully and independently. However, our recent extensive simulation work (Ogurtani and Akyildiz, 2004) on the grain boundary grooving and the cathode drifting shows that in the EM dominating regime v P 1 the groove depth has a finite asymptotic value, which is inversely proportional with the electron wind intensity parameter denoted by v, which will be defined in the next section. The slowing down trend in the groove tip displacement is also observed by Averbuch et al (2003b) in their recent but rather limited experiments, which are unfortunately too early terminated because of the extremely long computation time.…”