A new criterion of mask birefringence for polarized illumination

We propose a new criterion for mask birefringence in polarized illumination. Mask birefringence is one of the critical properties of polarized illumination, because the illumination polarization is disturbed by the birefringence of a mask substrate. From this point of view, the allowable mask birefringence has already been analyzed. In these analyses, only the absolute values of birefringence have been specified. As has been pointed out, the mask is a rotation retarder for the polarized illumination. Therefore, the angle of the fast axis of mask birefringence also affects the state of polarization. The new criterion of mask birefringence which we propose here adopts the angle of fast axis as well as the absolute value of birefringence. This new criterion correlates well with the printed critical dimensions (CDs). To demonstrate this, printed CDs were calculated as a function of birefringence. A lithography simulator was used to verify the fit of the new criterion. In this simulation, experimentally measured absolute values of birefringence and the angle of fast axis were used. The simulation showed that there was poor correlation between printed CDs and the absolute values of birefringence. On the other hand, the new criterion exhibited a good correlation with the printed CDs. This difference is attributed to the effect of the angle of fast axis.