A Novel Semi-Analytical Approach for Fast Electromigration Stress Analysis in Multi-Segment Interconnects

As integrated circuit technologies move below 10 nm, Electromigration (EM) has become an issue of great concern for the longterm reliability due to the stricter performance, thermal and power requirements. The problem of EM becomes even more pronounced in power grids due to the large unidirectional currents flowing in these structures. The attention for EM analysis during the past years has been drawn to accurate physics-based models describing the interplay between the electron wind force and the back stress force, in a single Partial Differential Equation (PDE) involving wire stress. In this paper, we present a fast semi-analytical approach for the solution of the stress PDE at discrete spatial points in multi-segment lines of power grids, which allows the analytical calculation of EM stress independently at any time in these lines. Our method exploits the specific form of the discrete stress coefficient matrix whose eigenvalues and eigenvectors are known beforehand. Thus, a closed-form equation can be constructed with almost linear time complexity without the need of time discretization. This closed-form equation can be subsequently used at any given time in transient stress analysis. Our experimental results, using the industrial IBM power grid benchmarks, demonstrate that our method has excellent accuracy compared to the industrial tool COMSOL while being orders of magnitude times faster.