Hierarchical Bayesian parameter estimation of the reliability of nanoscale Metallic Oxide Semiconductor (MOS) devices

Abstract

The successful fabrication and incorporation of metallic oxides into semiconductors has been a major milestone in the electronic industry. To increase the performance of micro processors, the number of transistors crammed into each micro processor chip has progressively increased. This has been made possible by the reduction (scaling) of transistor dimensions among which is the dielectric thickness. The reduction of the dielectric thickness has had severe reliability and performability implications and challenges, so it is imperative that models that predict dielectric reliability be developed. In this research, we present an integrated three-stage hierarchical Bayesian model for dielectric failure, to estimate the unknown parameters of the underlying reliability structure of a high-k Metal Oxide semiconductor (MOS) device failure. Hierarchical Bayes models have successfully been used in public health and related research, so we extend this application to dielectric failure analysis by incorporating the current MOS dielectric failure physics model into the failure probability function in the form of the Arrhenius-Weibull model. Previous statistical analyses of dielectric failure have used either classical parametric or nonparametric statistical models. The proposed physics of failure model gives meaning to the shape and scale parameters of the two-parameter Weibull distribution, and is used to estimate the dielectric characteristic life, the failure rate and acceleration factor, all of which are necessary to predict the life of a dielectric thin film. Markov Chain Monte Carlo methods are used to obtain the posterior results which are finally used to obtain the dielectric mean time to failure (MTTF). The Bayesian results are compared to the results from the maximum likelihood (ML) and least square error (LSE) estimation techniques and shown to have relatively narrower predicted MTTF confidence interval.