Redundancy-aware Electromigration checking for mesh power grids

Electromigration (EM) is re-emerging as a significant problem in modern integrated circuits (IC). Especially in power grids, due to shrinking wire widths and increasing current densities, there is little or no margin left between the predicted EM stress and that allowed by the EM design rules. Statistical Electromigration Budgeting (SEB) estimates the reliability of the grid by considering it entirely as a series system. However, a power grid with its many parallel paths has much inherent redundancy. In this paper, we propose a new model to estimate the MTF and reliability of the power grid under the influence of EM, which accounts for these redundancies. We refer to this as the mesh model. To implement the mesh model, we also develop a framework to estimate the change in statistics of an interconnect as its effective-EM current varies. The proposed algorithm is quite fast and has an overall observed empirical complexity of 0(n^1.4). The results indicate that the series model, which is currently used in the industry, gives a pessimistic estimate of power grid MTF and reliability by a factor of 3-4.