A MODEL FOR LINEWIDTH-DEPENDENT ELECTROMIGRATION LIFETIME AND ITS APPLICATION TO DESIGN RULE SCALING FOR NARROW INTERCONNECTS

Analytical formulae for linewidth-dependent electromigration lifetime, as represented by a log-normal distribution, are derived based on a linewidth-independent log-normal grain size distribution. This formulation can quantitatively explain the experimentally observed increase of both the Median-time-to-failure and standard deviation (sigma) as the linewidth decreases to become comparable to or less than the median grain size. Comparison between the theoretical prediction and experimental data for three metallization systems all show reasonable agreement. Due to its analytical nature, the model can also be applied to define design rules versus linewidth for a given metallization technology down to the submicron linewidth. Conditions in limiting the process variations in order to optimize the scaling of design rules are discussed.