General Statistical Model for Dielectric Breakdown Including Reverse Area Scaling - The Role of Area-Dependent Dynamic Competition

In this work, we present a general statistical model using the joint Weibull-Fréchet distribution for dielectric breakdown (BD) including the reverse area scaling trend reported recently [1], [2]. This model only uses four parameters and is capable of well capturing the experimental data. By demonstrating its equivalence to the physics-based statistical model [1], [2], we show it can quickly extract the parameters of the physics-based model. Moreover, it can be used in reliability prediction as we demonstrate the general applicability of this model to capture a wide variety of scaling trends from conventional to reverse area dependence of dielectric BD. We outline important notion of area dependent dynamic competition (ADDC) process and discuss various controversies involving modern modeling approaches to simulate BD filament formation in consideration of ADDC process.