Binary and phase-shifting image design for optical lithography

A number of pre-distorted mask design techniques for binary and phase-shifting masks are proposed. This approach is based on modeling the imaging mechanism of a stepper by the Hopkins equations and taking advantage of the photoresist nonlinear characteristics. 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 contour shapes of our 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.