Abstract
A new statistical model for electromigration failure in fine-line thin film conductors is developed in [1] by extending [2] to incorporate the statistics of microstructure and concomitant variations in the activation energy for grain boundary diffusion. The resulting distribution of time t to failure is well-approximated bywhere N is the number of line segments that are potential independent failure elements, 1μ and σ are, respectively, the mean and standard deviation of an assumed normal distribution of activation energy in grain boundaries, γ is a scaling constant, T is in degrees Kelvin, j is the current density in the line, p1 is the fraction of line segments for which exactly one grain boundary occurs between two blocking boundaries, and Φ is the standard normal cumulative distribution function. (Note: .)
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