An improved description of the dielectric breakdown in oxides based on a generalized Weibull distribution

Abstract

In this work, we address modal parameter fluctuations in statistical distributions describing charge-to-breakdown (QBD) and/or time-to-breakdown (tBD) during the dielectric breakdown regime of ultra-thin oxides, which are of high interest for the advancement of electronic technology. We reobtain a generalized Weibull distribution (q-Weibull), which properly describes (tBD) data when oxide thickness fluctuations are present, in order to improve reliability assessment of ultra-thin oxides by time-to-breakdown (tBD) extrapolation and area scaling. The incorporation of fluctuations allows a physical interpretation of the q-Weibull distribution in connection with the Tsallis statistics. In support to our results, we analyze tBD data of SiO2-based MOS devices obtained experimentally and theoretically through a percolation model, demonstrating an advantageous description of the dielectric breakdown by the q-Weibull distribution.

The Pulse Azimuth effect as seen in induction coil magnetometers located in California and Peru 2007–2010, and its possible association with earthquakes

“…The Weibull distribution has been used to model dielectric breakdown and conduction in oxides and polymers as in Costa et al (2006)and Dissado and Fothergill (1992). It has also been widely used for general failure rate modeling.…”

q-distributions in complex systems: a brief review

“…For example, new classes of generalized asymmetric distributions have been introduced which include q-Weibull as a special case [117,118]. q-Weibull has also been applied in the study of fractal kinetics [119], dieletric breakdown in oxides [120], relaxation in heterogeneous systems [121], ciclone victims and highway lengths [55] among others. …”

“…For example, if p(x, λ) is a Weibull distribution, p q (x) is given by a q-Weibull distribution [120]. Naturally, other forms for f (λ) may be considered to obtain alternative distributions.…”

Power-law behaviour in time durations between extreme returns

“…To unconditionally evaluate the existence of power-law behaviour in the duration between extreme events, we use the q-Weibull distribution, initially introduced and applied by Picoli et al (2003), Costa et al (2006) and Vuorenmaa (2006). The q-Weibull distribution has sufficient flexibility to be able to interpolate the Weibull and q-exponential distributions and, thus, cause the tail of the Weibull distribution to be thicker.…”

“…For β = 1, the Weibull distribution changes to the exponential distribution. The q-Weibull distribution is obtained through the classical Weibull model, reflected in equation (4), by substitution of the exponential function for a q-exponential (Costa et al 2006) function. The q-exponential function is defined as:…”