ANALYTIC MODEL FOR THE GRAIN STRUCTURES OF NEAR-BAMBOO INTERCONNECTS

Scaling of electromigration test results for near-bamboo interconnects from accelerated test conditions to service conditions requires an understanding of the microstructural characteristics of the interconnects. An analytic model has been developed that allows prediction of the average polygranular cluster lengths and the number of clusters in a line, given the linewidth, the line length, and the characteristics of the grain size distribution of the original film. Grain-structure characteristics have also been measured for lines patterned from computer-generated thin-film microstructures. The large-cluster-length tail of the polygranular cluster-length distribution is well fit by an exponential distribution function, which can be accurately predicted using our new analytic model. Polycrystalline clusters shorter than a critical length Lcr cannot fail due to electromigration-induced grain-boundary diffusion alone, so that when all clusters in a line are shorter than Lcr, there is a transition in failure mechanisms. The model can be used to calculate the number of clusters longer than Lcr as a function of the line and grain-structure characteristics, as well as a function of the current density. The current-density dependence of the median time to failure due to polygranular failure mechanisms in near-bamboo lines, as well as the transition current density at which the transition in failure mechanisms occurs are predicted. This transition current density depends on the linewidth and the line length, as well as the grain size and grain size distribution of the film from which the line was patterned. © 1994 American Institute of Physics.