Fast prediction of electromigration lifetime with modified mean-time-to-failure equation

Black's mean-time-to-failure (MTTF) equation has been applied to predict electromigration lifetime in electronics for decades. It is an empirical equation, and at least three sets of data tested under two temperatures and two current densities are needed to determine the parameter n, activation energy E, and pre-factor A in the equation. Based on Onsager's entropy production theory, we derived a modified MTTF equation, in which n = 2 becomes definite. The activation energy E is intrinsic for materials; for SnAg solder joints, we can take it as 1 eV. Therefore, we only need one set of data (one temperature and one current density) to determine the perfector A, for predicting the electromigration lifetime of the test samples. Our modified MTTF equation provides a fast and cost-saving method for accurate prediction of the electromigration lifetime for electronic products.