1.2.1 Experimental Lifetime Estimation

EM tests are carried out using simple structures and stress conditions which accelerate the EM failure. This can be performed by stressing an interconnect line at significantly higher current density and temperature than those found at use condition. Typically, current densities in the order of 1 to 10 MA/cm$^2$ are used, and the test temperature lies in the range from 170 to 350 $^\circ$C [19]. Under such conditions, interconnect failure is obtained much faster than it would be possible at use conditions. An important issue here is that the results from the EM experiments have to be related to the real operating conditions, which means that the lifetimes obtained from the accelerated tests have to be extrapolated to the use conditions. In addition, only a limited number of interconnect structures are tested, whereas often hundreds of millions of interconnects exist on a chip. Therefore, the extrapolation needs to take into account, how to assess on-chip reliability from the EM sample structures.

In copper interconnects EM failures are primarily caused by void growth at the cathode end of the line [20]. As the void grows, the electric current is forced to pass through the highly resistive barrier layer, which leads to an increase of the line resistance. When this increase reaches a given threshold value, the line is considered to have failed. In this way, the EM lifetime of a given interconnect structure is determined by monitoring its resistance change.

Due to the statistical character of EM lifetimes, it is necessary to carry out EM experiments on a number of test structures. The lifetimes obtained from these experiments are statistically analyzed and regularly presented in probability plots following a certain distribution which is characterized by a mean time to failure (MTF) and standard deviation ($\sigma$) [21].

EM lifetimes are normally described using a lognormal distribution [22]. However, it has been discussed whether this choice is the most appropriate one [23], and it is argued that EM lifetimes are more correctly described by a multi-lognormal distribution. This has been recently confirmed by several EM experiments [8,24,25]. It should be pointed out that the understanding of the electromigration lifetime distribution is crucial for the extrapolation of the times to failure obtained empirically from accelerated tests to real operating conditions, as performed by a modified form of the Black equation [19,22].