Determination of the acceleration factor between wafer level and package level electromigration test

The characterization and monitoring of electromigration performance is usually performed using wafer level or package level tests. These two types of test involve very different temperature gradient and current density conditions. These differences of stress condition may affect the determination of electromigration parameters, namely the activation energy, Ea, and the current exponent, n, as described in the empirical Black's law: MTF = A.j/sup -n/exp(Ea/kT). The apparent evolution of n and Ea is critical because it complicates the calculation of extrapolated lifetime. To elucidate this apparent inconsistency, we built a numerical model of the flux of matter in a copper line to simulate lifetime and acceleration factor corresponding to wafer and package level electromigration tests. Our numerical model is able to simulate TTF corresponding to electromigration tests on a wide range of current density (two orders of magnitude). The analysis of simulated TTF predicts that the error in Black's law parameters Ea and n may occur both from wafer level (high current density and Joule heating) and package level (low current density). As a consequence, we recommend taking into consideration temperature gradients as well as the Blech effect to extrapolate lifetime correctly.