Black's law revisited—Nucleation and growth in electromigration failure

摘要

It can be seen through this exercise that the problem of predicting electromigration failure at use conditions accurately is not quite as straightforward as we had been led to believe over the past 40 years. Both the accelerations due to current and temperature, the two variables at our disposal, are not as they seem. Unless the current exponent is exactly one or two, Black's law as defined in Eq. (2) is incorrect. The activation energy as customarily obtained through the use of Eq. (8) is also incorrect, however, regardless of the measured current exponent. The work involved in accurately determining the proper extrapolation from accelerated tests is quite involved and probably beyond the means of most engineering assessments. The least one can get away with is to determine the current exponent fit to Black's law (Eq. (2)) and determine how much of the measured lifetime must be discounted under the conservative assumption that nucle-ation of damage will be provided by thermal stress voiding. The time to growth of the damage to failure can then be estimated with the use of pure growth kinetics and the activation energy for diffusion along the expected pathway.