Accelerated Discrete Degradation Models for Leakage Current of Ultra-Thin Gate Oxides

Using degradation measurements is becoming more important in reliability studies because fewer failures are observed during short experiment times. Most of the literature discusses continuous degradation processes such as Wiener, gamma, linear, and nonlinear random effect processes. However, some types of degradation processes do not occur in a continuous pattern. Discrete degradations have been found in many practical problems, such as leakage current of thin gate oxides in nano-technology, crack growth of metal fatigue, and fatigue damage of laminates used for industrial specimens. In this research, we establish a procedure based on a likelihood approach to assess the reliability using a discrete degradation model. A non-homogeneous Weibull compound Poisson model with accelerated stress variables is considered. We provide a general maximum likelihood approach for the estimates of model parameters, and derive the breakdown time distributions. A data set measuring the leakage current of nanometer scale gate oxides is analyzed by using the procedure. Goodness-of-fit tests are considered to check the proposed models for the amount of degradation increment, and the rate of event occurrence. The estimated reliabilities are calculated at lower stress of the accelerated variable, and the approximate confidence intervals of quantiles for breakdown time distribution are given to quantify the uncertainty of the estimates. Finally, a simulation study based on the gate oxide data is built for the discrete degradation model to explore the finite sample properties of the proposed procedure.