Reliability Analysis of Isolation Structures for Integrated Circuits Based on the Beta Generalized Weibull Distribution
- 1School of Electronic and Electrical Engineering, Minnan University of Science and Technology, Quanzhou 362700, China
- 2School of Electronic and Electrical Engineering, Shanghai University of Engineering Science, Shanghai 201620, China
- 3Department of Computer, Control and Management Engineering, University of Rome La Sapienza, Via Ariosto 25, 00185 Rome, Italy
Abstract
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.
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BibTeX
@article{cheng2026reliability,
title = {{Reliability Analysis of Isolation Structures for Integrated Circuits Based on the Beta Generalized Weibull Distribution}},
author = {Wei Cheng and Hongqing Zheng and Wanqing Song and Piercarlo Cattani},
journal = {Fractal and Fractional},
year = {2026},
month = oct,
doi = {10.3390/fractalfract10100728},
url = {https://www.mdpi.com/2504-3110/10/10/728},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Reliability Analysis of Isolation Structures for Integrated Circuits Based on the Beta Generalized Weibull Distribution
AU - Wei Cheng
AU - Hongqing Zheng
AU - Wanqing Song
AU - Piercarlo Cattani
PY - 2026
DA - 2026/10/19
JO - Fractal and Fractional
DO - 10.3390/fractalfract10100728
UR - https://www.mdpi.com/2504-3110/10/10/728
AB - 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.
SN - 2504-3110
ER -