A statistical model for step and ramp voltage breakdown tests in thin insulators

Abstract

A spread is observed in times to breakdown when step or ramp voltage tests are applied to thin film insulators which have non-shorting breakdowns and which are cleared of weak spots. Following earlier work on sequences of breakdowns in liquids, we investigated the properties of the spread of observations in thin insulators with a statistical model. Probability density functions are derived for the times to breakdown for step and ramp tests, and a relation is given for the ratio of the mean times to breakdown for ramp and step tests. The results agree with experimental observations on the oxides of aluminum and hafnium. This indicates a randomness of the breakdown process and permits the calculation of ramp breakdown voltages from the measured step breakdown voltages. Quantitative agreement is not obtained for silicon dioxide, probably owing to the lack of independence in the location of consecutive breakdown events.