Analysis of applying time-dependent clustering model to BEOL TDDB

Recently, a time-dependent clustering model has been reported showing good agreement with multiple sets of experimental TDDB data by proper consideration of the percentile scaling of different areas (vertical translation in the Weibull scale) [1,2]. In this work, we investigate the scaling property (horizontal translation) of time-to-fail (T_FAIL) for different areas. Our results indicate that both the horizontal and vertical scaling properties for area transformation are preserved in the clustering model, showing its potential to replace the Weibull model. Moreover, we demonstrate the applicability of the time-dependent clustering model to bi-modal TDDB data, often encountered in practice. Finally, we develop a successive breakdown theory in the framework of the clustering model and compare it with experimental BEOL TDDB data.