Bayesian inference of a lifetime distribution parameter on the time-dependent dielectric breakdown with clustering defects

Abstract

In this study, we compared three statistical methods including the Bayesian inference to evaluate the lifetime distribution of time-dependent dielectric breakdown with clustered defects. Especially, we focused on the effect of the prior information of the Bayesian inference to obtain an accurate low cumulative failure probability of lifetime distribution. The prior information about the breakdown physics can give an appropriate range of shape parameter of the distribution function. In comparison with the conventional estimation methods, we investigated the influence of sample size and prior distribution on parameter estimation accuracy of the Bayesian inference.

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

“…In this case, the probability plot shows a convex upward shape. [9][10][11][12][13][14][15][16][17][18] In the semiconductor reliability domain, as mentioned above, the Weibull distribution is assumed for dielectric breakdown with a temporospatial homogeneousness. Particularly, the weakest link concept will correspond to the TDDB lifetime.…”

“…The applications of a TDC model that describes the non-Poisson characteristics of a lifetime applied to TDDB are introduced. The physical and statistical background of the modeling and the mathematical methods for the accurate parameter extraction [14][15][16][17][18] are introduced. These elements provide methods to analyze and evaluate the TDDB characteristics affected by complicated defect densities.…”

“…Methods addressing the sample size issue have been investigated by applying the multi-link test structure 17) and Bayesian inference 18) to the TDDB characteristics analysis. The former covers a wide range of cumulative probabilities with a small size data set by using the sudden-death test technique.…”

“…17) The application of the Bayesian inference is the other method to cover the trade-off issue, and has previously been proposed and investigated. 18) The Bayesian inference is a method that applies prior knowledge for the estimation of the distribution parameters and has become one of the common methods of machine learning. In the Bayesian inference, the probability of a hypothesis is updated by the Bayes' theorem as renewed information becomes available.…”

“…The effects of weak or strong prior information to a and b have been investigated on the TDC model to evaluate their effectivity. 18) The statistical accuracies of the three methods (MLE, two-step method, and Bayesian inference) were compared by Monte Carlo (MC) simulations as shown in Fig. 6.…”