A high-accuracy proximity effect correction method for high-precision masks has been developed to satisfy current and future requirements. In this paper, we explain the primary features of this method and the theories on which it is based. The developed formula for obtaining the optimum correction dose is expressed in the form of either iterations or an infinite series of functions. The advantage of this formula is that it quickly converges to the sought value, bringing about high-accuracy proximity effect correction with a high calculation speed. A coarse graining method (covering pattern density and representative figure methods) for reducing calculation time is explained. This method has been adopted for an EX-11 series and has been used for mask writing from the 180 nm design rule onward.

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A new formula for proximity effect correction is discussed. The formula is represented by a series expansion. When infinite terms are used, the formula gives accurate optimum correction doses. The correction accuracy of the new formula is evaluated for the worst case scenario and compared with the conventional formula. It is shown that (1) the new formula suppresses correction errors to less than 0.5% for the deposited energy and (2) dimensional errors are less than 4 nm, even if only the first 3 terms are calculated for critical patterns. By using the new formula, the proximity effect correction can be carried out with sufficient accuracy, even for making reticles of 1 Gbit or higher-capacity DRAMs.

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