Characterizing GHOST proximity effect correction effectiveness by determining the worst-case error

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Background proximity effect corrections such as GHOST and the proposed SCALPEL correction technique have been analyzed to determine how well they can perform in situations where the correction dose distribution is not ideal. A technique has been developed that evaluates the largest possible correction dose error by determining the worst-case exposure pattern. This pattern is found to be unlikely to occur in integrated circuit patterns, so that the dose errors found in realistic situations are expected to be much smaller. For Gaussian shaped GHOST correction energy distributions, the worst-case pattern resembles a disk or a bull’s eye. The optimal correction dose distribution has a width parameter of about 90% of the backscatter width. The worst-case background dose error is less than +/−2% for a backscatter coefficient of 0.40. For a correction dose that resembles a disk of constant intensity, the worst-case error is typically larger than the case of a Gaussian shape. The smallest worst-case error occurs with a correction disk radius of 1.2 times the backscatter range for a backscatter coefficient of 0.50. The smallest worst-case error is +/−10% or one half of that, +/−5%, for practical pattern density ranges. The SCALPEL correction dose profile is ring shaped and the worst-case background error can be nearly as large as the backscatter coefficient. The worst-case error concept is used to search for the optimum ring shape; a worst-case error as small as +/−3% is possible with the appropriate correction ring characteristics.