There is considerable interest in performing a simulation study to fabricate attenuated phase-shifting mask (Att-PSM). In this study, a simulation work has been performed using matrix method to calculate the relative transmittance and the amount of phase shift of the light through the phase-shifting mask. However, it was found that the average film composition changed with the deposition time. Accordingly, the optical constants were found to be a strong function of the film thickness. Therefore, the relationship between the deposition parameters (e.g. deposition time, gas flow rate ratio) and the optical constants (e.g. refractive index and extinction coefficient) were rearranged to extract the empirical formula for the optical constants in terms of the film composition. For verification of this simulation study, the phase shifter was fabricated based on this simulation result, which was found to have transmittance of 8% and phase shift of 180˚. Consequently, a reliable optimum condition for DUV Att-PSM was obtained. Moreover, the stability of $CrF_x$ films was investigated by SEM, FT-IR, AES, WDS, and optical micrograph study.
