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Voltage-based electromigration immortality check for general multi-branch interconnects

As VLSI technology features are pushed to the limit with every generation and with the introduction of new materials and increased current densities to satisfy the performance demands, Electromigration (EM) is projected to be a key reliability issue for current and future VLSI technologies. Existing EM signoff mainly relies on current density-based assessment using Black's equation and Blech product. This model does not work well for multi-branch interconnect wires as the stresses developed in each wire segment is not independent of one another. In this paper, we present a novel and fast EM Immortality check for general multi-branch interconnect trees. Instead of using current density as the key parameter as in traditional methods, the new method estimates the EM-induced stress in general multi-branch interconnects based on the terminal voltages or potentials. It can be viewed as the Blech product for multi-branch interconnects for fast check of EM immortality of wires. Besides, this voltage-based EM (VBEM) assessment technique can naturally comprehend the impact of the topology of the wire structure on EM-induced stress. As a result, this new VBEM analysis method is very amenable to EM violation fixing as it brings new capabilities to the physical design stage. The VBEM stress estimation method is based on the fundamental steady-state stress equations. This approach eliminates the need for complex look-up tables for different geometries and can be implemented in CAD tools very easily as we demonstrate on real design examples. We show that its solution is consistent with the physics-based dynamic EM stress evaluations from the numerical analysis by COMSOL.