Analytical equation predicting the forbidden pattern pitch for phase-shifting mask

Abstract

In order to produce various kind of circuit pattern in short-term cycle, mask-less exposure using DMD(digital mirror device)-mask is useful. Although not only fine resolution but also large DOF(depth of focus) can be obtained by using PSM(phase shifting mask), there exists forbidden pitch region for PSM. While the pattern pitch of PSM becomes fine, it cannot be resolved at a certain pitch and it will be resolved again at a finer pattern pitch. This un-resolvable region is called forbidden pitch region. It has been time consuming to predict this region by numerical calculation. Applying PSM to various fields, we should predict the region simply. In this paper, we derive analytical equations which give the optimal NA(Numerical Aperture) and finest resolution and also reveal forbidden region. In addition, we confirm the validity of analytical equation by numerical calculation using PROLITHTM. This result will be useful to apply PSM in practice.