Time to Electromigration-induced Failures
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The times to electromigration-induced failures are lognormally distributed as given by, [1]

        times to electromigration-induced failures ---------------------- [2887a]
where,
         σ -- The standard deviation of ln(t),
         t -- The time to electromigration-induced failure,
         t50 -- The median time to failure (MTTF).          

MTTF is related to the number, type, and distribution of structural defects [2].

The failure distribution function for the lines, Gsp(t), can be given by [3],

        times to electromigration-induced failures ---------------------- [2887b]
where,
         Np -- The number (=w/d) of parallel units,
         Ns -- The number of units which is approximately equal to the line length divided by the grain size, l/d.
        times to electromigration-induced failures ---------------------- [2887c]

f(z) is given by Equation 2887a.


         

 

 

 

 

 

 

[1] LaCombe, D.J. and Parks, E.L., The distribution of electromigration failures, 24th Annual Proceedings Reliability Physics (1986) 1-6   DOI: 10.1109/IRPS.1986.362103.
[2] Attardo, MJ; Rosenber.R , Electromigration Damage in Aluminum Film Conductors, Journal of Applied Physics,  41(6)  2381.  DOI: 10.1063/1.1659233.
[3] Cho, J. and Thompson, C. V., Grain size dependence of electromigration-induced failures in narrow interconnects, 54(25), 2577 (1989).

 

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