Fault probability and confidence interval estimation of random defects seen in integrated circuit processing Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/xs55mf72r

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  • Various methods of estimating the fault probabilities based on defect data of random defects seen in integrated circuit manufacturing are examined. Estimates of fault probabilities based on defect data are less costly than those based on critical area analysis and are potentially more reliable because they are based on actual manufacturing data. Due to limited sample size, means of estimating the confidence interval associated with these estimates are also examined. Because the mathematical expressions associated with defect data-based estimates of the fault probabilities are not amenable to analytical means of obtaining confidence intervals, bootstrapping was employed. The results show that one method of estimating the fault probabilities based on defect data proposed previously is not applicable when using typical in-line data. Furthermore, the results indicate that under typical fab conditions, the assumption of a Poisson random defect distribution gives accurate fault probabilities. The yields as predicted by the fault probabilities estimated from the limited yield concept and kill ratio and those estimated from critical area simulation are shown to be comparable to actual yields observed in the fab. It is also shown that with in-line data, the FP estimated for a given inspection step is a weighted average of the fault probabilities of the defect mechanisms operating at that inspection step. Four bootstrapped based methods of confidence interval estimation for fault probabilities of random defects are examined. The study is based on computer simulation of randomly distributed defects with pre-assigned fault probabilities on dice and the resulting count of different categories of die. The results show that all four methods perform well when the number of fatal defects is reasonably high but deteriorate in performance as the number of fatal defects decrease. The results also show that the BCA (bias-corrected and accelerated) method is more likely to succeed with a smaller number of fatal defects. This success is attributed to its ability to account for change of the standard deviation of the sampling distribution of the FP estimates with the PP of the population, and to account for median bias in the sampling distribution.
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