Effect of grain structure on the current-density exponent in the black equation for Al-alloy interconnects

Abstract

Lifetimes of Al-based interconnects against electromigration-induced failures have been predicted by a well-known empirical relation (Black equation). The numerical value of the current-density exponent (n) contained in the Black equation has commonly been accepted as 2. However, the n value often deviates from 2, depending on the interconnect geometry or the applied current density. The work reported here shows that n also varies as a function of the microstructure. We have explored the Black equation over a wide range of interconnect grain structures. As they evolve from homogeneous polygranular lines to "quasi-bamboo" lines and eventually to almost perfect "bamboo" lines, the n value increases from 1.9 to 2.4 and finally to 3.1, respectively. The significance of the experimental results is discussed based on the microstructural mechanisms of electromigration failures.