For nonzero mean-to-target (MTT), critical dimension (CD) recovery to the nominal CD in the reference region by simply changing the dose cannot be achieved in the other regions with different pattern densities. The mask error enhancement factor (MEEF) and the exposure latitude (EL) depend on the pattern density, which cause the final CD mismatched to the nominal CDs. The formulaic expression of the mask margin for the MTT and uniformity is constructed as a function of the MEEF, the EL, and the nominal CD tolerance.
Line and space (L/S) pattern of 200 nm pitch size and isolated space pattern of 120 nm are designed and chosen as dense and sparse patterns, respectively. Simulation is performed using Gaussian convolution method, and the diffusion length is found to be 40 nm by fitting it to the measured data. The designed L/S pattern and isolated space pattern are exposed on chrome-on-glass mask using ArF scanner with 0.75NA and annular illuminating condition. The nominal CDs of L/S and isolated space pattern are 105 nm and 115 nm, respectively. The MEEF and the EL are measured to be 2.45 and 6.6 nm-cm2/mJ for L/S Pattern, and 1.86 and 8.60 nm nm-cm2/mJ for isolated space pattern, respectively. The summation values of the MTT and uniformity are calculated to be 8.6 nm with the tolerance of 5 nm for both patterns, and 6.7 nm with the tolerance of 3 nm for L/S pattern and 5 nm for isolated space pattern.
The mask margin for the MTT and uniformity proves to be changed for the variation of the nominal CD, or the feature size with the nominal CD fixed. By properly optimizing the conditions of illumination condition, mask type to be sued, and the feature size, the allowable mask tolerance for the MTT and uniformity could be increased.