A practical predictive formalism to describe generalized activated physical processes

A predictive formalism is developed that is applicable to the large class of activated physical systems described by a differential equation of the generic form: ∂n(φ,t)/∂t =−n(φ,t)F(t) exp(−(φ−R(t))/A(t)). Practical techniques to predict the behavior of activated physical systems for arbitrary time-dependent environments are both intuitively and mathematically developed. Useful techniques to experimentally determine the initial distribution of activation energies, utilizing arbitrary time-dependent laboratory environments, are presented. A number of fundamental results regarding the correct use and interpretation of common diagnostic techniques, such as Arrhenius plots, are derived. It is shown how the predictive results significantly enhance the ability to quantitatively evaluate the reliability of physical systems whose rate-limiting mechanisms are activated processes obeying the above differential equation. Specific issues regarding integrated circuit reliability are examined as potential applications of this predictive formalism, including time-dependent dielectric breakdown, metal electromigration, nonvolatile memory retention, annealing of radiation-induced trapped charge, and thin ferroelectric film switching properties.