Filamentary model of dielectric breakdown

Abstract

A dielectric breakdown model based on the phenomenological description of the nucleation and growth of filaments is proposed. This description involves different characteristic times according to the interfacial or bulk nature of the growth processes. The resulting time to breakdown distribution presents Weibull or bimodal shape according to the relative values of those characteristic times. In particular, the variation in the Weibull slope with thickness is observable when the interfacial process characteristic time is the larger. Bimodal shapes are observable when the characteristics times are in the same range and the surface scaling of the distributions influences the apparent Weibull slopes. The model is compared to experimental constant voltage stress and linear ramp voltage stress measurements made on metal insulator metal and metal oxide semiconductors structures. The physical parameters extracted are discussed. Breakdown electric fields are derived as functions of temperature, dielectric thickness, and dielectric permittivity consistently with experimental trends. The electric field acceleration factors are also derived and depend on dielectric thickness.