Analytical Modeling of Transient Electromigration Stress based on Boundary Reflections

Traditional methods that test for electromigration (EM) failure in multisegment interconnects, over the lifespan of an IC, are based on the use of the Blech criterion, followed by Black's equation. Such methods analyze each segment independently, but are well known to be inaccurate due to stress buildup over multiple segments. This paper introduces the new concept of boundary reflections of stress flow that ascribes a physical (wave-like) interpretation to the transient stress behavior in a finite multisegment line. This can provide a framework for deriving 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 proposed method is shown to have excellent accuracy, through evaluations against the FEM solver COMSOL, as well as scalability, through its application on large power grid benchmarks.