1-D model of current distribution and resistance changes for electromigration in layered lines

We present a one-dimensional (1-D) analytical model incorporating contact resistance to calculate the current distribution between an Al line and refractory metal underlayer in a drift velocity measurement structure for electromigration. The current profile so calculated is more accurate than the usual assumption that the current all flows in the Al portion, and it should give a more accurate and reliable relation between drift velocity and current density. It should also be useful in correlating local current density with voiding. Various experimentally observed voiding processes are included in the model; they reproduce and predict different types of changes in total line resistance, most notably the step structure observed in electromigration.