Some practical physics-based formulas have been derived to make quick estimates of imaging performances in lithographic systems. These formulas have a simple structure so that they can be used in mathematical worksheets or, if desired, on a pocket calculator. Formulas have been derived to predict the printing of dense lines, bright field isolated lines, and dark field isolated spaces in positive resist. They are for exposures from binary masks and give exposure latitude, focus depth, and change in critical dimension. These parameters are also derived as a function of fading of the aerial images in lateral and focal directions. Validity has been checked with simulations. It proved that, in cases of the aerial image fading and of focus depth evaluation, only a few adjustment parameters were needed to obtain a reasonably good match with simulations. A table with all basic imaging parameters and their dependence on disturbances such as fading is included.
"Formulas for lithographic parameters when printing isolated and dense lines," Journal of Micro/Nanolithography, MEMS, and MOEMS 4(4), 043001 (1 October 2005). https://doi.org/10.1117/1.2140247