Electromagnetic study of a photolithography setup for periodic masks and application to nonperiodic masks

Abstract

We develop a rigorous electromagnetic analysis to study the field diffracted by a metallic or dielectric grating made of rectangular rods, lying over a stratified media. The analysis generalizes the modal theory of perfectly conducting lamellar gratings combined with the R-matrix propagation algorithm in order to avoid numerical instabilities, thus allowing treatment of layers and gratings of arbitrary thickness. We then study the field map obtained under the conditions stated in a previous patent that described a process for casting on a support the faithful reproduction of a mask pierced with periodically distributed slits. We make a systematic study of the influence of the various parameters (incidence, mark–space ratio, groove spacing, groove depth, polarization, conductivity of the metal) on the field map below the mask. We discover a large tolerance over the parameters, close to the values stated in the patent. The result is that the setup described in the patent valid for periodic maps can be used for duplicating nonperiodic masks (e.g., linear Fresnel zone plates) as well as chirped gratings or gratings with nonrectilinear grooves.