Reliability Analysis of Isolation Structures for Integrated Circuits Based on the Beta Generalized Weibull Distribution

The reliability analysis of integrated circuit (IC) isolation structures (ISs) faces two challenges: how to accurately describe the distribution of time-to-failure (TTF) data, and how to obtain the TTF distribution under actual working conditions (AWCs). To address these issues, this paper introduces the flexible five-parameter Beta Generalized Weibull (BGW) distribution, which can represent the five characteristic failure-rate shapes (IFR, DFR, CFR, BFR and UBT). The sign of the hazard derivative is analyzed through Glaser’s eta-function theorem together with the asymptotic behavior of the hazard rate at the origin and at infinity; this yields exact, necessary-and-sufficient parameter conditions for each shape, with the origin controlled by the product aγω and the tail controlled by γ. A TTF model based on the BGW distribution is then proposed to predict the TTF distribution under AWCs, and it is proved analytically that a change of stress affects only the scale parameter δ, leaving all shape parameters unchanged. Because this invariance was previously stated as an assumption, it is verified empirically on the time-dependent dielectric breakdown (TDDB) data using per-level Weibull shape estimates with bootstrap confidence intervals, a Kruskal–Wallis test on standardized failure times, and a parametric-bootstrap likelihood-ratio test within the BGW family; all three tests support stress-invariant shapes. The reliability function is recast as a convergent infinite series, with the correct beta-integral kernel and an explicit ratio-test bound. Finally, the effectiveness and superiority of the method are verified using TDDB TTF data, and the untested 3800 V condition is predicted from the fitted linear voltage-acceleration model.