Electromigration model for the prediction of lifetime based on the failure unit statistics in aluminum metallization

Abstract

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 consists of failure units in parallel and series, can predict both the median time to failure (MTTF) and the deviation in the time to failure (DTTF) in Al metal lines. The model can describe them only qualitatively. In our model, both the probability function of the failure unit in single grain segments and polygrain segments are considered instead of in polygrain segments alone. Based on our model, we calculated MTTF, DTTF, and activation energy for different median grain sizes, grain size distributions, linewidths, line lengths, current densities, and temperatures. Comparisons between our results and published experimental data showed good agreements and our model could explain the previously unexplained phenomena. Our advanced failure unit model might be further applied to other electromigration characteristics of metal lines. (C) 2003 American Institute of Physics.