Electromigration lifetime as a function of line length or step number

The dependence of electromigration-induced (EM) failure time on line length and step number in the line has been investigated. Theoretical equations for the dependence are derived assuming that EM failure obeys the Weibull failure distribution function. The EM failure time distribution of 2.4 mu m-wide AlSi(1%) lines of different lengths or with different step numbers agreed well with the equations. Also confirmed experimentally was the theoretical prediction that the shape parameter m in the Weibull distribution function is the key parameter for estimating the EM lifetime of an LSI product based on lifetime measurements of test structures. A lower EM resistance at the step location than that of the flat lines has been investigated quantitatively and has been interpreted in terms of the difference in step coverage, joule heating, grain size, and stress. A unifying equation to include both straight and step locations for EM lifetime is derived.<>