PARADOXICAL PREDICTIONS AND A MINIMUM FAILURE TIME IN ELECTROMIGRATION

A paradox arises when the two-parameter log-normal distribution is used to predict early electromigration lifetimes of a two-level structure with Ti-AlCu-Ti stripes and interlevel W stud-vias. The paradox is a direct consequence of the observed increase in the log-normal sigma (σ) as the current density decreases and/or as the maximum allowed resistance change increases. The increase in σ implies that the first failures from equal and large sample sizes are expected to occur at low current densities rather than at high current densities. Similarly, for example, samples at relatively low cumulative failure are expected to fail at high levels of resistance change before failing at low levels of resistance change. This apparent paradox is resolved by testing a large set of samples and fitting the failure data to the three-parameter log-normal distribution. The third parameter, an incubation time or a minimum time required before failure can occur, is shown to increase as the maximum allowed resistance change increases.© 1995 American Institute of Physics.