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

TL;DR

This paper reviews statistical fiber bundle models and their application to physics-based reliability analysis of thin-film dielectrics, introducing new models and analyzing breakdown distributions in circuit systems.

Contribution

It provides a comprehensive overview of fiber bundle models, proposes new assumptions, and applies the formalism to dielectric breakdown in circuit reliability analysis.

Findings

Derived load-sharing rules from electrical laws for circuit breakdowns.

Obtained breakdown distribution and Gibbs measure for series circuits.

Compared various breakdown distributions and analyzed size effects in reliability systems.

Abstract

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 load-sharing 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.