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We presented a model for the line-width-dependent grain structure statistics in bamboo interconnects. We then showed, using an electromigration simulation, that grain orientation-dependent interface diffusivities constitute a likely mechanism contributing to the variabilities in lifetimes observed in experiments.

I. INTRODUCTION

It has been well established in experiments that geometry and microstructure have a direct impact on the electromigration-limited reliability of on-chip Al-based interconnects.1– 4 Interconnects can have polygranular segments for which there are continuous grain boundary paths along the length of the interconnect, and bamboo segments, in which one or more grains span the width of the line, and grain boundaries are perpendicular to the line direction. In near-bamboo Al-based interconnects, electromigration (EM)-induced diffusion occurs much faster along the grain boundaries in the polygranular segments than in the bamboo segments, where diffusion occurs primarily along the interfaces. 5,6 It has been previously shown that the coupling between the difference in diffusivities of polygranular clusters and bamboo segments, and their geometry-dependent length distributions, can account for the magnitudes of the variations of electromigration-limited lifetimes.7,8 Post-patterning annealing of polygranular interconnects can result in grain growth leading to purely bamboo structures for which EM lifetimes are governed solely by surface or interface diffusion.5,6 In this case, the variability in EM lifetimes observed in experiments on Al-based interconnects with bamboo structures,9 and Cu-based interconnects,9,10 in which interface diffusion dominates even in non-bamboo structures, is not well understood. One possible contributor to this variation is grain-structure-related variations in interface diffusivities. In this article, we present a 2D grain-growth simulation for the width-dependent grain-length distribution in lines having bamboo structures resulting from postpatterning annealing of polygranular interconnects (see Fig. 1). We then simulate the effects of grain-structurerelated variations in the surface diffusivities by assuming that surface or interface diffusivity varies with grain orientation in accordance with a Read-Shockley model.12 J. Mater. Res., Vol. 16, No. 2, Feb 2001

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We finally show, using an EM simulation,13 along with published values for surface diffusion in Cu,14 that a grain-orientation-dependent diffusivity can account for the lifetime variations observed experimentally in Albased and Cu-based interconnects with bamboo grain structures.9–11 II. BAMBOO GRAIN STRUCTURE STATISTICS

Using a 2D simulation of curvature-driven grain growth, GGSim,15,16 we simulated the development of bamboo structures in polygranular interconnect strips with different widths. This transformation is depicted in Fig. 1. We have shown elsewhere16 that 2D normal grain growth in thin films leads to a uniquely defined grain structure, evolving i