Theoretical MEF calculation for periodic patterns

Current reduction projection exposure tools with a large numerical aperture lens can fabricate fine features with smaller than exposure wavelength using several resolution enhancement techniques. In such subwavelength lithography, a precise control of the mask becomes critical because a degradation of the image due to proximity effects become much larger than would be expected from the normal reduction ratio of the projection lens. The mask pattern errors are amplified at the wafer and the ratio of this amplification is called MEF (mask error enhancement factor). In this paper, we show that the MEF can be calculated theoretically based on the Fourier optics and we clarify the behavior of MEF for periodic line patterns. The MEFs related to alternate phase shift mask (PSM), attenuated PSM, and binary mask are evaluated.