Mask-roughness-induced line-edge roughness: rule of thumb

Much work has already been done on how both the resist and line-edge roughness (LER) on a mask affect the final printed LER. What is poorly understood, however, is the extent to which system-level effects such as mask surface roughness, illumination conditions, and defocus couple to speckle at the image plane and factor into current LER limits. We propose a "rule-of-thumb" simplified solution that provides a fast and powerful method to determine mask-roughness-induced LER. Using a one-time aerial image modeling of the mask surface roughness to obtain clear-field speckle statistics, the LER for any feature can quickly be calculated from a simple analytic extension using feature-specific image log slope. We investigate how the clear-field speckle is scaled by the intensity at the line edge, and mathematically couples to LER in the simplified case of a knife edge. We apply this relation to nested lines and spaces and compare this analytic LER to fully simulated values. We present modeling data on an older generation mask with a roughness of 230 pm as well as the ultimate target roughness of 50 pm. Moreover, we consider feature sizes of 50 and 22 nm and show that as a function of correlation length, the LER peaks at the condition that the correlation length is approximately equal to the resolution of the imaging optic. (C) 2010 Society of Photo-Optical Instrumentation Engineers. [DOI: 10.1117/1.3497607]