Electromigration: Lognormal versus Weibull distribution

Basavalingappa, Adarsh; Passage, Jennifer M.; Shen, Mingyue; Lloyd, J. R.

doi:10.1109/iirw.2017.8361224

Cited by 14 publications

(7 citation statements)

References 6 publications

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“…Moreover, competing distribution models are approximated using the generalized gamma distribution (GENG), which is widely used for reliability analysis. [18][19][20][21] The gamma distribution for V min is verified and compared with the GENG model. Finally, a simple method for V min estimation of large-scale SRAM macros by extrapolating the gamma distribution fitted line with few data is provided.…”

Section: Introductionmentioning

confidence: 95%

Estimation of minimum operating voltage in fully depleted SOI SRAM cells using gamma distribution

Mizutani

Takeuchi

et al. 2022

Jpn. J. Appl. Phys.

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Minimum operating voltages (Vmin) of every cell on a 32kb fully-depleted (FD) SOI static random access memory (SRAM) macro are successfully measured. The competing Vmin distribution models, which include the gamma and log-normal distribution, are approximated using the generalized gamma distribution (GENG). It is found that Vmin of the cells follow the gamma distribution. This finding gives a simple method to estimate worst Vmin of an SRAM macro by measuring few samples and make linear extrapolation from the gamma distribution.

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Section: Introductionmentioning

confidence: 95%

Estimation of minimum operating voltage in fully depleted SOI SRAM cells using gamma distribution

Mizutani

Takeuchi

et al. 2022

Jpn. J. Appl. Phys.

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“…This suggests that the lognormal distribution is appropriate for the lifetime distribution of the degradation processes with combinations of random rate constants that relate multiplicatively, like fatigue crack growth in metals. 5) In the field of reliability physics of electron devices, the lognormal distribution is used for the analysis of the electromigration of BEOL interconnects and solder bumps [27][28][29][30][31][32] because the proportional effect model suits the failure mechanism. The reliability of the LSI chip is evaluated using the lognormal distribution for segments.…”

Section: Lognormal Distributionmentioning

confidence: 99%

“…The lognormal assumption for segments has been validated experimentally in many previous studies. 27,28,31,32) Based on this assumption, the chip electromigration reliability estimation has been implemented in many design tools. However, because the circuit and layout design of the chip cannot be certain until the final phase of the product development, the design check can only be performed after they are determined.…”

Section: Background Of Chip-level Lifetime Estimationmentioning

confidence: 99%

“…64) Basavalingappa et al investigated the fit of the segment lifetime to the distributions by considering the grain microstructure and elastic anisotropy of Cu. 32) They concluded that even though the Weibull distribution may appear to fit the observations better when all data points are considered, the lognormal distribution will be more appropriate for predictive extrapolations by separating the failure modes. Furthermore, they added that if the electromigration-based failure in any number of "N" identical configurations are being considered, the use of extreme value distribution might be more appropriate than the lognormal distribution.…”

Section: Studies For Current Density and Lifetime Distribution Of Ele...mentioning

confidence: 99%

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Applications of lifetime distribution functions with two shape parameters for reliability analysis in advanced interconnect technologies: a brief review

Yokogawa¹

2020

Jpn. J. Appl. Phys.

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In this brief review, applications of lifetime distribution functions with two shape parameters for reliability analysis are introduced in advanced interconnect technologies. For the time-dependent dielectric breakdown analysis, the time-dependent clustering model is applied. Suppressing the trade-off between two shape parameters is required for an accurate estimation of the clustering parameter. Some statistical techniques, including the sudden-death test structure and the Bayesian inference, are reviewed. For simple electromigration evaluation on a chip-level, an adaption of the generalized Gamma distribution is proposed. The impacts of the circuit scale and the segment variations are investigated with the Monte-Carlo technique. This review suggests that variation control will become ever more important for advanced interconnect technology developments.

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“…One may also refer to Johnson et al [18] for several applications of this distribution in various life testing experiments. This distribution is treated as an alternative model to some known distributions like Weibull, gamma and generalized exponential models, see for instance, Basavalingappa et al [10], Raqab et al [33], and Jia et al [17]. Crow and Shimizu [12] discussed the importance of Bayesian inference for the lognormal distribution in various life testing studies.…”

Section: Introductionmentioning

confidence: 99%

Bayesian Analysis for Lognormal Distribution under Progressive Type-II Censoring

Singh¹,

Tripathi²,

Wu³

2018

HJMS

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In this paper, we consider the problems of Bayesian estimation and prediction for lognormal distribution under progressive Type-II censored data. We propose various noninformative and informative priors for the unknown lognormal parameters and compute the Bayes estimates under squared error loss function. Importance sampling technique and OpenBUGS are taken into consideration for the computational purpose. Further, we predict lifetimes of both censored and future samples under one-and two-sample prediction frameworks. We also compute the corresponding Bayes predictive bounds. A simulation study is conducted to compare the performance of proposed estimates and a real data set is analyzed to illustrate applications of this study. Finally, a conclusion is presented.

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Electromigration: Lognormal versus Weibull distribution

Cited by 14 publications

References 6 publications

Estimation of minimum operating voltage in fully depleted SOI SRAM cells using gamma distribution

Estimation of minimum operating voltage in fully depleted SOI SRAM cells using gamma distribution

Applications of lifetime distribution functions with two shape parameters for reliability analysis in advanced interconnect technologies: a brief review

Bayesian Analysis for Lognormal Distribution under Progressive Type-II Censoring

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