Monte Carlo Calculations Based on the Generalized Electromigration Failure Model

The dependence of electromigration failure-time on line width and current density was studied using Monte Carlo calculations. In constructing the model used here, A total of three factors were considered: the metallurgical properties of the film, the thermal process during failure propagation, and the stress induced mass flow. In the study on line width dependence, median time to failure (t50) was revealed to decrease as line width decreased to about median grain size, and to increase steeply as the line width decreased further, in good agreement with previous experiments. A wide variety of values assigned to an exponential factor (n) in current density dependence of t50 (t50∝ J-n) was successfully explained by introducing the effective length where a stress gradient has built up.