Analysis of the successive breakdown statistics of multilayer Al₂O₃/HfO₂ gate stacks using the time-dependent clustering model

The successive oxide failure statistics theory that arises from the clustering model is used for investigating the time-to-breakdown distributions of Al₂O₃/HfO₂-based nanolaminates. These gate dielectrics in metal-insulator-semiconductor structures are intended to combine a high injection barrier material (Al₂O₃) with a high-K material (HfO₂). When a constant voltage is applied to the structures, the current-time characteristics exhibit stepwise changes that correspond to the sequential opening of multiple conducting channels across the dielectric film. This study demonstrates that a clustering-based approach successfully describes the ordered breakdown statistics associated with the appearance of these conducting channels. Deviations of the experimental data from the expected Weibull statistics at the high percentiles are accounted for by introducing the so-called clustering factor. The origin of the deviations is attributed to the high dispersion of the initial leakage current value and consequently to the initial conducting properties of the oxide film.