Analytic modeling for the limit of mask mean-to-target from the photolithographic standpoint

Abstract

The critical dimension (CD) deviation from a nominal CD induced by the mask mean-to-target (MTT) is normally compensated by adjusting the exposure dose. However, the compensation is not accomplished to both cell and peripheral patterns which have different pitch sizes. In general, the exposure dose is adjusted to obtain the nominal CD of the cell pattern which has smaller pitch size than the peripheral pattern. The final CD of the cell pattern recovers its nominal CD by changing the exposure dose while that of the peripheral pattern does not but the final CD of the peripheral pattern should be located within a given tolerance range. Based on this idea, an analytic model for the limits of the mask MTT is proposed in this letter. Mask error enhancement factors and exposure latitudes for an island and two types of line and space patterns are obtained experimentally. Then, arguments adopted to derive the analytic expression for the MTT are assessed by comparing measured peripheral CDs with calculated ones for three types of patterns. Results are shown to match within 2% of nominal CDs under the different mask MTTs of 13.1, 19.7, and 26.2 nm at the mask scale (4×). The mask MTT specifications for three types of patterns are calculated at the CD tolerances of ±4 nm. The calculated limit of the mask MTT is ±4.3 nm for the island pattern. ±9.8 nm and ±9.3 nm of mask MTT limits are obtained for two types of line and space patterns.