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 eta and shape parameter beta. We clarified the precondition that the TDC model holds when term eta(B) 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.