Modeling the electromigration failure time distribution in short copper interconnects
DwyerVincent
2009
The electromigration EM lifetime in short copper interconnects is modeled using a previously
developed means of generating realistic interconnect microstructures combined with the
one-dimensional stress evolution equation of Korhonen et al. J. Appl. Phys. 73, 3790 1993 . This
initial analysis describes the void nucleation and subsequent growth in lines blocked at one end and
terminated with a pad at the other. For short copper interconnects, the failure time is largely spent
on void growth, and, for sufficiently short lines (≤ 50 mm), the growth is largely steady state. This
allows for the development of a simple expression for the variation of the failure time with
microstructure. Assuming that the diffusion activation energies are normally distributed, the
permanence property of summed lognormals leads to a roughly lognormal distribution for EM
failure times. Importantly for EM design rules, linear extrapolation on lognormal plot is found to
slightly underestimate interconnect reliability.