Monte Carlo simulation of electromigration in polycrystalline metal stripes

Abstract

We have developed a Monte Carlo simulator of the electromigration process in polycrystalline metal stripes. Stripes with different average grain size can be generated with Voronoi tesselation, and mapped onto a network of resistors. The proposed model includes the major role played by grain boundaries and by the current density redistribution within the stripe following void formation. Simulations of stripes with different grain sizes and different widths are shown, and a few expressions for the failure probability are compared on the basis of their capability of reproducing the experimental results. In addition, electromigration noise has been computed, recovering the characteristic 1/f γ (γ ≈ 2) behaviour. The substantial qualitative agreement between our calculations and the experimental results is a convincing test of the capability of the model proposed to include the relevant physics.

Noise and reliability in simulated thin metal films

“…This spectra can easily be explained as the effect of small independent step increases in the resistance which are induced by single damage events [20]. While this independence is reasonable for the initial phase of the electromigration damage and leads to random walk of resistors and therefore to 1/f 2 spectrum, in the advanced stages of stripe damage a degree of correlation arises, which leads to the well known c fluctuations [12,20].…”

“…The FFT is applied to moving time windows, in order to track the evolution of noise spectrum as the electromigration damage proceeds [20]. Fig.…”

“…While this independence is reasonable for the initial phase of the electromigration damage and leads to random walk of resistors and therefore to 1/f 2 spectrum, in the advanced stages of stripe damage a degree of correlation arises, which leads to the well known c fluctuations [12,20].…”

Development of a Multi-Scale Electromigration Simulator Based on a Combination of Ultra Accelerated Quantum Chemical Molecular Dynamics and Kinetic Monte Carlo Methods Application to Cu Interconnects Lifetime Simulation

“…[3][4][5][6][7][8] On the theoretical side, the key challenge is to bridge the scale gap between LSI devices and individual atomic processes enabling thus the manipulation of realistic interconnects lengths and time scales in order to predict their lifetimes. A large number of studies have been performed separately, one is the macroscopic prediction of line failure phenomenon under specific operation conditions [9][10][11][12] and the other is microscopic understanding of EM, which consists in the diffusion of metal atoms caused by electron wind forces 3,4,13,14) respectively. However few of these studies combine both the macroscopic and microscopic phenomena in order to achieve a better solution to the problem, yet, studies considering multi-scale simulations linking the device scale behavior with the atomic level dynamics are critical in the design of electronic devices.…”