Maximum Likelihood Estimation for Failure Analysis of SRAM Cells Using . . .

The numerical evaluation of the maximum-likelihood estimate of a subset of mixture proportions, Siam J. [15] LOQO an efficient implementation of an interior-point method for large scale linear and/or quadratic programming problems, available via ftp://elib.zib-berlin.de A comparison of iterative maximum-likelihood estimates of the parameters of a mixture of two normal distributions under three different types of sample, Biometrics, 29, pp. 761-770, 1973 [24] B.M. Hill, Information for estimating the proportions in mixtures of exponential and normal distributions, 6 Summary In this paper we have described an iterative ML estimation method for failure analysis. We have numerically compared the ML estimate with other two methods, the least squares and enu-meration. The results showed that both the least squares and the enumeration estimators didn't coincide with MLEs. We analyzed the ill-conditioned problem of a DCM, and illustrated some "good" or "bad" DCM structures. The elements of the normalized DCM should be well-separated to guarantee accurate MLEs for defect classes. We also showed how to derive sample size needed to ensure the expected accuracy of ML estimation. Finally, to illustrate the effectiveness of the iterative ML algorithm we have provided an experimental example by performing our ML estimation on a real SRAM cell with the assumption that each electrical fault represents a fault behavior. The ML estimates with such an assumption provide a lower bound on number of samples needed. A comparison of new and old algorithms for a mixture estimation problem, A generic method to develop a defect monitoring system for IC processes, 20 To avoid fortuitous phenomena of using only one experiment, we performed 20 more experiments using the same assumption and approach. The results are shown in Table 8. From that table, one can easily see that the estimation accuracies in all experiments accord with the expected ones with a sample size of 500. TABLE 8 MLEs for p(d), means of p(d) and average standard deviations of the twenty experiments short poly-break ndiff poly-pdiff poly-m1 poly-poly ndiff-ndiff m1-m1 ndiff-m1 m1-m2 pdiff-pdiff ndiff ndc poly pdiff pdc m1 polyc p(d)_1 p(d)_3 p(d)_4 p(d)_6 p(d)_7 p(d)_9 p(d)_10 p(d)_12 p(d)_13 p(d)_15 p(d)_16 p(d)_18 p(d)_19 average stand. dev. m2 or m2c 19 we assume the probability distribution in Table 6 is the true value for each defect class, the standard deviation of each estimated defect class probability is less than 0.03 (see Table 7). This meets our expectations. Fig. 3 is a histogram of …