An Analytical Solution for Transient Electromigration Stress in Multisegment Straight-line Interconnects Based on a Stress-wave Model

This work presents an analytical approach for analyzing electromigration (EM) in modern technologies that use copper dual damascene (Cu DD) interconnects. In these technologies, due to design rule and methodology constraints, wires are typically laid out unidirectionally in each metal layer; since EM in Cu DD interconnects do not cross layer boundaries, the problem reduces to one of analyzing EM in multisegment interconnect lines. In contrast with traditional empirical methodologies, our approach is based on physics-based modeling, directly solving the differential equations that model EM-induced stress. This article places a focus on interconnect lines, for reasons described above, and introduces the new concept of boundary reflections of stress flux that ascribes a physical (wave-like) analogy to the transient stress behavior in a finite multisegment line. This framework is used to derive analytical expressions of transient EM stress for lines with any number of segments, which can also be tailored to include the appropriate number of terms for any desired level of accuracy. The approach is applied to both the nucleation phase and the postvoiding phase on large power grid benchmarks. These experiments demonstrate excellent accuracy as compared to accurate numerical solution, as well as linear complexity with the number of segments for evaluating stress at a specified point and time.