A failure model for electromigration based on the “failure unit model” was presented for the prediction of lifetime in metal lines. The failure unit model, which consisted of failure units in parallel and series, could predict both the median time-to-failure and the deviation in the time-to-failure in Al metal lines. The model could describe them only qualitatively. In the present model, both the probability function of the failure unit in single grain segments and polygrain segments were considered instead of in polygrain segments alone. Based on the present model, median time-to-failure, deviation in the time-to-failure and activation energy were calculated for different median grain sizes, grain size distributions, line-widths, line lengths, current densities, and temperatures. Comparisons between the present results and published experimental data showed good agreements and this model could explain some previously unexplained phenomena. The advanced failure unit model might be further applied to other electromigration characteristics of metal lines.

Electromigration Model for the Prediction of Lifetime Based on the Failure Unit Statistics in Aluminum Metallization. J.H.Park, B.T.Ahn: Journal of Applied Physics, 2003, 93[2], 883-92