Binary and phase shifting mask design for optical lithography

The authors propose a number of pre-distorted mask design techniques for binary and phase-shifting masks. Their approach is based on modeling the imaging mechanism of a stepper by the Hopkins equations and taking advantage of the contrast-enhancement characteristics of photoresist. Optimization techniques such as the branch and bound algorithm and simulated annealing algorithm are used to systematically design pre-distorted masks under incoherent and partially coherent illumination. Computer simulations are used to show that the intensity contour shapes and developed resist shapes of their designed mask patterns are sharper than those of conventional masks. The designed phase-shifting masks are shown to result in higher contrast as well as sharper contours than binary masks. An example of phase conflicting masks designed with the algorithm is shown to outperform a simple intuitive design. This example indicates that a fairly general design procedure consisting of alternating phase shifts and their optimized phase-shift masks is a viable candidate for future phase-shifting mask design