(An) advanced statistical model for the lifetime prediction due to electromigration failure and an improved fast method for the reliability evaluation in metal lines

Abstract

The electromigration characteristics with various microstructures, geometries and dimensions in Al lines were evaluated. And a modified statistical model based on “unit failure model” was proposed and verified. In addition, a new test method for fast monitoring the defective metal lines was proposed and evaluated in Al and Cu lines. The effects of the sputtering condition and in-situ or ex-situ annealing on the MTTF (median time to failure) and DTTF (deviation time to failure) have been determined experimentally. The more reliable Al-1%Si-0.5%Cu line was performed at high deposition power, high deposition temperature and high annealing temperature. The results indicated that the more reliable metal line could be achieved with less the amount of impurities (nitrogen, hydrocarbon and etc.), larger grain and denser film. The electromigration failures of Al lines with stacked barrier metal (Ti, TiN) were studied. The MTTF increases as the stacked layer of refractory metal is added. Also, the effect of dimensions (W, L) and geometries of the metal line such as straight line, bended lines, and topology steps on MTTF and DTTF have been determined experimentally. These results showed the same or similar trend of the results reported previously by other authors. In order to predict the electromigration lifetime of metal lines, we needed a quantitative general model. Thus a modified failure model for electromigration based on the “failure unit model” was proposed in metal lines. The “failure unit model”, which consists of failure units in parallel and series, can predict both the MTTF and 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 various median grain sizes, grain size distributions, line widths, line length...