Using Statistics of Extremes for Electromigration and Time-Dependent Dielectric Breakdown

This paper deals with the extreme values statistics use for metal interconnect and dielectric reliability in microelectronics. For electromigration reliability on Cu lines, experimental failure times are obtained by using an especially designed test structure (multilink) allowing determination of successive lower failure times on a large set of samples. It is shown that the experimental statistical distributions of minima failure times using our multilink structures are deductible from the usual single Cu lines lognormal distribution with the help of extreme values and order statistics. The analytical transformations from single interconnect lognormal distribution to the successive first, second, and third minima failure time distributions are derived with the help of scaling parameters. In particular, the first failure time's distribution is a Weibull distribution whose parameters are a simple expression of the total number of links and the parent lognormal distribution parameters. Since time-dependent dielectric breakdown follows also Weibull statistics, the origin of parent distribution and its analytical possible form are similarly discussed in the framework of extreme values statistics. The statistics of successive breakdown are also derived from order statistics.