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.
Brittany M. McClinton,
Patrick P. Naulleau,
"Mask-roughness-induced line-edge roughness: rule of thumb," Journal of Micro/Nanolithography, MEMS, and MOEMS 9(4), 041208 (1 October 2010). https://doi.org/10.1117/1.3497607