A relationship between statistical time to breakdown distributions and pre-breakdown negative differential resistance at nanometric scale

Using an ultra-high vacuum Conductive atomic force microscopy (C-AFM) current voltage, pre-breakdown negative differential resistance (NDR) characteristics are measured together with the time dependent dielectric breakdown (TDDB) distributions of Si/SiON (1.4 and 2.6 nm thick). Those experimental characteristics are systematically compared. The NDR effect is modelled by a conductive filament growth. It is showed that the Weibull TDDB statistic distribution scale factor is proportional to the growth rate of an individual filament and then has the same dependence on the electric field. The proportionality factor is a power law of the ratio between the surfaces of the CAFM tip and the filament's top. Moreover, it was found that, for the high fields used in those experiments, the TDDB acceleration factor as the growth rate characteristic is proportional to the Zener tunnelling probability. Those observations are discussed in the framework of possible breakdown or forming mechanism.