Modeling and simulation of successive breakdown events in thin gate dielectrics using standard reliability growth models

The application of constant electrical stress to a metal-insulator-semiconductor (MOS) or metal-insulator-metal (MIM) structure can generate multiple breakdown events in the dielectric film. Very often, these events are detected as small jumps in the current-time characteristic of the device under test and can be treated from the stochastic viewpoint as a counting process. In this letter, a wide variety of standard reliability growth models for this process are assessed in order to determine which option provides the best simulation results compatible with the experimental observations. For the generation of the breakdown event arrivals, two alternative stochastic methods for the power-law Poisson process are investigated: first, the inversion algorithm for the cumulative distribution function and second, an on-the-fly method based on the so-called rejection algorithm. Though both methods are equivalent, the first one is more appropriate for data analysis using spreadsheet calculations while the second one is highly suitable for circuit simulation environments like LTSpice. The connection of the selected nonhomogeneous Poisson process with the Weibull model for dielectric breakdown is also discussed.