Modeling the electromigration failure time distribution in short copper interconnects

Abstract

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.