Temperature-dependent standard deviation of log(failure time) distributions

The distributions of failure times at accelerated life-test temperatures are often analyzed assuming a constant-σ model, where σ is the standard deviation of log(failure times). Recent experimental and theoretical studies of laser degradation, time-dependent dielectric breakdown, and electromigration suggest that σ is temperature-dependent. The author derives a general relationship for temperature-dependent σ from the Arrhenius relation. The relationship is used to analyze published electromigration data. The analysis suggests that the correlation coefficient between the activation energy and log(pre-exponential factor in the Arrhenius relation) close to -1. An example illustrates the use of the relationship to validate the electromigration design rule of a hypothetical microcircuit technology. The author argues that assuming a constant σ could result in an invalid design rule