Monte Carlo Based Weibull Lifetime Uncertainty Calculation and Statistical Comparison of Process Module Changes for Lifetime Improvement

摘要

Weibull statistics are used in generation of gate oxide lifetimes from time dependent dielectric breakdown (TDDB) data. However, error bounds for the Weibull generated predicted lifetimes are not usually presented. Statistical methods to judge the impact of process improvements on Weibull lifetimes are also presented. Each of three electric fields was used to generate 1000 points point sets with probability of occurrence determined from a fixed, known underlying distribution. This distribution represents a population of points with a Weibull distribution. From the 1000 points, a sample of 10 to 25 points was randomly selected for each of the three applied electric fields. The subset of points were placed in rank order, and analyzed using the Maximum Likelihood procedure. These steps were repeated to obtain Monte Carlo based statistical information about the impact of sample size on our knowledge of the population. Additionally, similar methods were used to determine the experimental design required to statistically valid information regarding the impact of process changes on gate oxide lifetime.