A new aspect of time-dependent clustering model for non-uniform dielectric TDDB

We investigated the time-dependent clustering (TDC) model for time-dependent dielectric breakdown (TDDB) of non-uniform dielectrics and revealed for the first time that the TDC model is a compound Weibull model that is expressed as a superposition of Weibull distributions. The Weibull model has two statistical parameters, scale parameter η and shape parameter β We clarified the precondition that the TDC model holds when term ηβ of the Weibull model is distributed according to an inverse-gamma distribution. By using our finding, we proposed a new method to directly estimate the variations of electric field and effective space from TDDB data. We found that the corresponding electric field distribution is a generalization of extreme value distribution, which is a natural consequence since the lifetime is determined by the maximum value of the electric field.