A finite weakest-link model of lifetime distribution of high-k gate dielectrics under unipolar AC voltage stress

Le, Jialing

doi:10.1016/j.microrel.2011.09.010

Cited by 14 publications

(15 citation statements)

References 33 publications

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“…Le, Bažant and Bazant (2009), Le (2012) and Bažant and Le (2017) (Chap-ter 14) proposed a subcell model for high-gate dielectrics. Here, the dielectric is viewed as a parallel circuit of cells and where each cell is a series circuit of nanocapacitors subcells.…”

Section: Cell Models For Dielectricsmentioning

confidence: 99%

“…), extreme value asymptotics suggest that the BD statistics would be approximately Weibull for long chains. Lack of fit of the Weibull is attributed to size effects of the finite length of the chain where Le (2012) and Bažant and Le (2017) referred to the model as a finite weakest link model.…”

Section: Cell Models For Dielectricsmentioning

confidence: 99%

“…Statistical analyses of their data for Figures 3, 6, and 14 regarding the BD formalism are given in Section 8. (The data for Figure 14 was kindly provided by Le (2012) who used this data in his analysis of his load-sharing cell model. The data from Figures 3 and 6 were reconstructed from the figures since J. C. Lee was not successful in locating this data.…”

Section: Part II Introduction: Statistical Aspectsmentioning

confidence: 99%

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Current Overview of Statistical Fiber Bundles Model and Its Application to Physics-based Reliability Analysis of Thin-film Dielectrics

Gleaton¹,

Han²,

Lynch³

et al. 2021

Preprint

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In this paper, we present a critical overview of statistical fiber bundles models. We discuss relevant aspects, like assumptions and consequences stemming from models in the literature and propose new ones. This is accomplished by concentrating on both the physical and statistical aspects of a specific load-sharing example, the breakdown (BD) for circuits of capacitors and related dielectrics. For series and parallel/series circuits (series/parallel reliability systems) of ordinary capacitors, the load-sharing rules are derived from the electrical laws. This with the BD formalism is then used to obtain the BD distribution of the circuit. The BD distribution and Gibbs measure are given for a series circuit and the size effects are illustrated for simulations of series and parallel/series circuits. This is related to the finite weakest link adjustments for the BD distribution that arise in large series/parallel reliability load-sharing systems, such as dielectric BD, from their extreme value approximations.An elementary but in-depth discussion of the physical aspects of SiO 2 and HfO 2 dielectrics and cell models is given. This is used to study a loadsharing cell model for the BD of HfO 2 dielectrics and the BD formalism. The latter study is based on an analysis of Kim and Lee (2004)'s data for such dielectrics. Here, several BD distributions are compared in the analysis and proportional hazard regression models are used to study the BD formalism. In addition, some areas of open research are discussed.

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Section: Cell Models For Dielectricsmentioning

confidence: 99%

Section: Cell Models For Dielectricsmentioning

confidence: 99%

Section: Part II Introduction: Statistical Aspectsmentioning

confidence: 99%

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Current Overview of Statistical Fiber Bundles Model and Its Application to Physics-based Reliability Analysis of Thin-film Dielectrics

Gleaton¹,

Han²,

Lynch³

et al. 2021

Preprint

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“…The observed deviations were similar as for the finite weakest-link chain for quasibrittle materials. A rigorous mathematical analogy with the electronic breakdown has been identified [123,124], and the theory adapted from strength probability has been shown to describe well the deviations. Further refinement has been presented by J.-L.…”

Section: Some Ramifications and Structural Engineering Applicationsmentioning

confidence: 99%

Design of quasibrittle materials and structures to optimize strength and scaling at probability tail: an apercu

Bažant

2019

Proc. R. Soc. A.

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The objective in materials or structure design has been to maximize the mean strength. However, as generally agreed, engineering structures, such as bridges, aircraft or microelectromechanical systems must be designed for tail probability of failure less than 10 −6 per lifetime. But this objective is not the same. Indeed, a quasibrittle material or structure with a superior mean strength can have, for the same coefficient of variation, an inferior strength at the less than 10 −6 tail. This tail is unreachable by histogram testing. So, one needs a rational theory, physically based and experimentally verified indirectly, which is feasible by size effect. Focusing on the results at the writer's home institution, this inaugural article (written three years ex post facto ) reviews recent results towards this goal, concerned with quasibrittle materials such as concretes, rocks, tough ceramics, fibre composites, bone and most materials on the micrometer scale. The theory is anchored at the atomic scale because only on that scale the failure probability is known—it is given by the frequency of breakage of bonds, governed by the activation energy barriers in the transition rate theory. An analytical way to scale it up to the macroscale representative volume element (RVE) has been found. Structures obeying the weakest-link model are considered but, for quasibrittle failures, the number of links, each corresponding to one RVE, must be considered as finite. The result is a strength probability distribution transiting from Weibullian to Gaussian, depending on the structure size. The Charles-Evans and Paris laws for subcritical crack growth under static and cyclic fatigue are also derived from the transition-rate theory. This yields a size-dependent Gauss–Weibull distribution of lifetime. Close agreement with numerous published test data is achieved. Discussed next are new results on materials with a well-defined microscale architecture, particularly biomimetic imbricated (or staggered) lamellar materials, exemplified by nacre, a material of astonishing mean strength compared to its constituents. This architecture is idealized as a diagonally pulled fishnet, which is shown to be amenable to an analytical solution of the strength probability distribution. The solution is verified by million Monte Carlo simulations for each of the fishnets of various shapes and sizes. In addition to the classical weakest-link and the fibre-bundle models, the fishnet is found to be the third strength probability model that is amenable to an analytical solution. The nacreous architecture is shown to provide an additional major (greater than 100%) strengthening at the 10 −6 failure probability tail. Finally, it is emphasized that the most important consequence of the quasibrittleness, and also the most effective way of calibrating the 10 −6 tail, is the size effect on the mean structural strength, which permeates all formulations.

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“…Although the applications described above are for the mechanical breakdown of a system or network, the ideas extend to other types of systems. See, for example, Duxbury and Leath () and Le () who studied the failure of electrical networks using load‐sharing formulations.…”

Section: A Gibbs Measure Representation For Load‐sharing Systemsmentioning

confidence: 99%

What is the shape of a bundle? An analysis of Rosen's fibrous composites experiments using the chain‐of‐bundles model

Gleaton

Lynch

2018

Scandinavian J Statistics

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In the 1960s, W. B. Rosen conducted some remarkable experiments on unidirectional fibrous composites that gave seminal insights into their failure under increasing tensile load. These insights led him to a grid system where the nodes in the grid were ineffective length fibers and to model the composite as something he called a chain‐of‐bundles model (i.e., a series system of parallel subsystems of horizontal nodes that he referred to as bundles), where the chain fails when one of the bundles fails. A load‐sharing rule was used to quantify how the load is borne among the nodes. Here, Rosen's experiments are analyzed to determine the shape of a bundle. The analysis suggests that the bundles are not horizontal collection of nodes but rather small rectangular grid systems of nodes where the load‐sharing between nodes is local in its form. In addition, a Gibbs measure representation for the joint distribution of binary random variables is given. This is used to show how the system reliability for a reliability structure can be obtained from the partition function for the Gibbs measure and to illustrate how to assess the risk of failure of a bundle in the chain‐of‐bundle model.

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A finite weakest-link model of lifetime distribution of high-k gate dielectrics under unipolar AC voltage stress

Cited by 14 publications

References 33 publications

Current Overview of Statistical Fiber Bundles Model and Its Application to Physics-based Reliability Analysis of Thin-film Dielectrics

Current Overview of Statistical Fiber Bundles Model and Its Application to Physics-based Reliability Analysis of Thin-film Dielectrics

Design of quasibrittle materials and structures to optimize strength and scaling at probability tail: an apercu

What is the shape of a bundle? An analysis of Rosen's fibrous composites experiments using the chain‐of‐bundles model

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