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Two of the key performance parameters in the manufacture of photomasks and reticles are composite placement and composite overlay. Multipoint fitting of the placement and overlay errors is typically used in specifying the performance of the printing tool, whereas two-point fitting is more commonly used in the mask-production environment. In this study, Monte Carlo simulation techniques are used to compare the placement results that may be expected using the two methods. Mask yields are evaluated sing the maximum observed error as the primary metric, because this criterion is prevalent in the industry. The influence of several factors is examined, including number of sample points, size of test pattern, and the presence of systematic printing errors. The baseline test case consists of a 7 X 7 grid of points with an extent of 132-nm square with two additional alignment marks separated in the x direction by 144 mm, and random normally distributed errors with standard deviation (sigma) . For this case, the expected maximum error at 95% mask yield from a two-point alignment is approximately 4.5 (sigma) , and (tau) equals 1.3, where (tau) is defined as the ratio of the maximum error for two-point versus multipoint fitting. The expected maximum error depends logarithmically on the number of sample points, and (tau) decreases as the number of points increases. A sinusoidal systematic error in the printing system greatly degrades the yield using two-point alignment but has relatively little effect upon the yield using multipoint alignment. Similarly, an orthogonality mismatch between the printing and metrology tool causes (tau) to increase significantly, whereas a scale mismatch decreases (tau) . It is also demonstrated that the result from two-point alignment has more statistical uncertainty than that from the multipoint methodology, and thus multipoint alignment is more accurate in determining the expected performance of a given printing system from a limited set of sample masks.
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