Modeling of the Structure and Reliability of Near-Bamboo Interconnects

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Abstract
When interconnect feature sizes (e.g., widths) and grain sizes are comparable, their average electromigration-lifetime increases. However, reliability increase occurs for a population of lines only if microstructural weak links, such as polygranular clusters, become unlikely throughout the population. Lifetime statistics and grain structure statistics are linked in a way which must be understood in order to take advantage of lifetime improvements through line-width-dependent and line-length-dependent current density limits. An analytic model has been developed which allows calculation of the polygranular cluster length distribution as a function of line width, line length and current density, given continuous-film median grain sizes and grain size deviations. A simple analytic model for the effect of post-patterning anneals on polygranular cluster length distributions is also presented. These models are shown to be consistent with detailed computer simulations of grain structures and grain structure evolution in interconnects. Improved grain structure models will enable less-conservative integrated circuit design practice, allowing design of higher performance circuits.