Static Electromigration Analysis for Signal Interconnects

With the increase in current densities, electromigration has become a critical concern in high-performance designs. Typically, electromigration has involved the process of time-domain simulation of drivers and interconnect to obtain average, RMS, and peak current values for each wire segment. However, this approach cannot be applied to large problem sizes where hundreds of thousands of nets must be analyzed, each consisting of many thousands of RC elements. In this paper, we propose a static electromigration analysis approach. We show that under conditions that are typically met by VLSI interconnects, the charge transfer through wire segments of a net can be calculated directly by solving a system of linear equations, thereby eliminating the need for time domain simulation. Also, we prove that under these conditions the charge transfer through a wire segment is independent of the shape of the driver current waveform. From the charge transfer through each wire segment, the average current is obtained directly, as well as approximate RMS and peak currents. We account for the different possible switching scenarios that give rise to unidirectional or bi-directional current by separating the charge transfer from the rising and falling transitions, and also propose approaches for modeling multiple simultaneous switching drivers. The results on a number of industrial circuits demonstrate the accuracy and efficiency of the approach.