An investigation of electromigration induced void nucleation time statistics in short copper interconnects

The stress evolution model (SEM) of Korhonenet al., is used to calculate the void nucleation time in a large number of short interconnects lengths up to 50 um. Finite element calculations show that the effect of the nonlinearity in the SEM model is small, and that a mesh size of the order of the grain size is quite adequate to give accurate simulation results. Via failure is the only mode considered in the current calculations, however the gain in simulation time over other solution methods means that more complex situations, possibly including void dynamics, may be modeled in future in this way. Using normal mass-lumping methods the analysis is isomorphic to the voltage development on a random RC chain, so standard methods from very large scale integrated static timing analysis may be used to obtain dominant time constants at each mesh point. This allows the distribution of nucleation times to be obtained as a function of the distributions of line parameters. Under the assumption of a lognormal grain size distribution and a normal distribution of diffusion activation energies, the nucleation time distribution is shown to be close to lognormal