Computer simulation of electromigration in thin-film metal conductors

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Abstract
A model is presented for simulating electromigration in thin‐film metal conductors. The backfluxes are calculated explicitly in each of the grain boundaries using concentration and stress gradients resulting from the initial electromigration flux. The stress‐dependent diffusivity term is also directly included in the formulation. It is assumed that the main cause of the flux divergence is the grain structure of the conductor and that these divergences occur at the triple‐point junctions of the grain boundaries. Time‐to‐failure and classic resistometric analyses of five conductors are performed. Results indicate that current‐density exponent of n≊2 should be used in time‐to‐failure analysis. This is due to the localized stress migration and diffusion acting against the electromigration force throughout the period of the conductor lifetime. A direct correlation between the time to failure (TTF) and relative rate of resistance change Rrc was found when all conductors and stress conditions were considered together. This relationship is of the form TTF=0.223R−1.11rc and indicates that resistance measurements can be used in producing lifetime parameters for use in providing reliability rules for conductor design.