A fast and accurate method for interconnect current calculation

Abstract

As VLSI technology continues to scale down, the electromigration problem has become one of the dominant factors in determining system reliability. This problem is caused by high current density flowing in the metal interconnect. Therefore, current evaluation is a crucial concern in IC design. SPICE level circuit simulators are excellent for doing current calculation; however, their running times are too expensive to be used repeatedly in design synthesis loops. In this paper, we propose an efficient approach for the interconnect current calculation. This method is based on moment matching but does not need high order moments. It only needs to traverse the RC tree once to get the mean current value of every segment, while traversing the tree once more is enough for the RMS current calculation, and two more traversals is sufficient for the peak current calculation. We apply our method to a larger number of interconnects getting close-to-SPICE accuracy at significantly faster runtimes. In particular, applying the method to 17,387 wire segments in the clock tree of a commercial IC, we obtained that the average deviation error of mean current is 0.0569%, average RMS current error is 0.703% and average peak current error is 6.552%. It took 28 hours for HSPICE to get the current value of all the wire segments and it only took our method 156 seconds.