Maximum Likelihood Estimation for Yield Analysis

A generic method to develop a defect monitoring system for IC processes, A comparison of new and old algorithms for a mixture estimation problem, The numerical evaluation of the maximum-likelihood estimate of a subset of mixture proportions, [19] 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 I DDQ Table 2 gives the ML estimation results of the two strategies. The solution of strategy two is more accurate than that of strategy one since strategy two takes all observed fault signatures into full account. Note that strategy one's DCM is an ideal one in the sense that each fault signature corresponds to a single defect type, but the results in Table 2 show that yield analysis using this DCM will be inaccurate. In a previous experiment [18] in which faulty signatures of all possible realistic defects that may occur in a SRAM cell were predicted case-by-case, approximately 61% of the defects cause a single cell fault signature in an SRAM array. It is clear that including single cell fault signatures in yield analysis, even though many different defect types may cause these fault signatures, is necessary to correctly identify the underlying probability distribution of yield detractors. In this paper, we have described the ML estimation methodology for yield analysis. The methodology consists of three steps. The first step is to run a fault extractor and a circuit simulator on an IC to extract the defect type to fault signature mapping with the corresponding conditional probabilities. The condition number of the resulting DCM can be used to measure the effectiveness of this circuit for yield analysis. Then after the ICs are fabricated, they are tested and the fault signature count recorded. Given the IC's DCM and fault signature count, the underlying probability distribution of the defect types is extracted using an iterative ML estimation algorithm. Similar procedures have been used in previous yield analysis research [8,13,7]. This paper describes two potential sources of inaccuracies in them and provides solutions. The first is that using a least squares fit does not always provide an accurate maximum likelihood estimate. The second is that excluding a subset of the fault signatures from the analysis will make diagnostic results inaccurate. Two illustrative examples were provided. Figure 6. (a) Defect type to fault signature matrices of strategy one and two, (b) DCM of strategy one, (c) …