A percolative approach to electromigration in metallic lines

Abstract

We present a stochastic model which simulates electromigration damage in metallic interconnects by biased percolation of a random resistor network in the presence of degradation and recovery processes. The main features of experiments including Black's law, times to failure distribution, current threshold for the onset of electromigration, etc are properly reproduced. Compositional effects showing up in early resistance changes measured on Al-0.5%Cu and Al-1%Si lines are also studied.

Resistance Noise Near to Electrical Breakdown: Steady State of Random Networks as a Function of the Bias

“…In particular, a strong nonlinearity emerges in the pre-breakdown region which is also characterized by a non-Gaussian noise. The results compare well with measurements of electrical breakdown in composites 2,22,19 and in semicontinuous metal films 16 and with electromigration experiments in metallic lines 26,25 .…”

“…The second process consists of recovering the insulating defects with probability W R,n = exp(−E R /K B T n ), where E R is an activation energy characteristic of this second process 25,49 . Thus, the first process consists in a percolation of broken resistors within a network of active resistors.…”

“…This defect generation process is taken to occur in competition with an opposite process, named defect recovery, which mimics the healing mechanisms. Electromigration of metallic lines 4,26 instability of the electrical properties of composites or semicontinuous metal films 2,3 , 13-19 , 22,23 or soft dielectric breakdown of ultra-thin oxides 4,29 , are examples of phenomena that can be successfully described by this approach 25,31,[49][50][51] . In the case of electromigration phenomena, for example, the defect generation corresponds to the formation of voids induced by the electronic wind, while the defect recovery is related to the void healing due to mechanical stress and thermal gradients inside a metallic film 4,26 .…”

Monte Carlo simulation of electromigration phenomena in metallic lines

“…To check the ability of the model to describe EM experiments, simulations are performed on Al-0.5%Cu lines [7]. A significant aspect related to the electrical failure is the damage pattern, which evidences the correlations among different failing regions just before the complete failure.…”

“…Figure 2 reports a typical damaged pattern obtained for a network of sizes 40 × 40 with the following parameters chosen according to the experimental conditions of Ref. [7]:…”