A theoretical analysis to estimate the effect of shot noise on CDU is induced from optical imaging perspectives combined
with quantum theory, and is studied for 193-nm, EUV, and electron beam lithography. We found the CDU variation
from shot noise is related to the number of particles absorbed in the printed area and to the image log slope (ILS). Hence,
the CDU variation contributed by shot noise gets worse when the technology node advances from 45- to 32-, 22-, and
15-nm, EUV with higher ILS is no exception. For e-beam lithography, we are interested in the values of ILS calculated
from array structures with different pitches, backscattering, wafer-stage movement, and raster-scan writing.
We propose a useful methodology, called phase-defocus (P-D) window, to express the mutual dependence of Alt-PSM mask structure and the wafer process window of the pattern-position shift caused by phase error and intensity imbalance. The P-D window was predicted and optimized with a 2-D mask with effective phase and transmission by simulations. We further used rigorous E-M field simulations to correlate the 3-D mask structure to those optimized conditions. Moreover, experiments were performed with four kinds of mask structures and the best Alt-PSM structure was obtained and used to suggest the mask fabrication performance based on P-D window analysis. In order to understand the influence of mask fabrication on patterns with various densities, the common P-D window is proposed. Using the P-D window, the optimized condition was achieved with a maximum process margin for the mask and wafer. In addition, the P-D window is used to quantify the scattering effect coming from the topographical mask and determine the effective 180° for the iso-focal condition.