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Electromigration (EM) is a key reliability issue in deeply scaled technologynodes. Traditional EM methods first filter immortal wires using the Blechcriterion, and then perform EM analysis based on Black's equation on theremaining wires. The Blech criterion is based on finding the steady-statestress in a two-terminal wire segment, but most on-chip structures areconsiderably more complex. Current-density-based assessment methodologies,i.e., Black's equation and the Blech criterion, which are predominantly used todetect EM-susceptible wires, do not capture the physics of EM, but alternativephysics-based methods involve the solution of differential equations and areslow. This paper uses first principles, based on solving fundamental stressequations that relate electron wind and back-stress forces to the stressevolution in an interconnect, and devises a technique that analyzes any generaltree or mesh interconnect structure to test for immortality. The resultingsolution is extremely computationally efficient and its computation time islinear in the number of metal segments. Two variants of the method areproposed: a current-density-based method that requires traversals of theinterconnect graph, and a voltage-based formulation negates the need for anytraversals. The methods are applied to large interconnect networks fordetermining the steady-state stress at all nodes and test all segments of eachnetwork for immortality. The proposed model is applied to a variety of tree andmesh structures and is demonstrated to be fast. By construction, it is an exactsolution and it is demonstrated to match much more computationally expensivenumerical simulations.

A Linear-Time Algorithm for Steady-State Analysis of Electromigration in General Interconnects