Rigorous diffraction analysis using geometrical theory of diffraction for future mask technology

Abstract

Advanced lithographic techniques such as phase shift masks (PSM) and optical proximity correction (OPC) result in a more complex mask design and technology. In contrast to the binary masks, which have only transparent and nontransparent regions, phase shift masks also take into consideration transparent features with a different optical thickness and a modified phase of the transmitted light. PSM are well-known to show prominent diffraction effects, which cannot be described by the assumption of an infinitely thin mask (Kirchhoff approach) that is used in many commercial photolithography simulators. A correct prediction of sidelobe printability, process windows and linearity of OPC masks require the application of rigorous diffraction theory. The problem of aerial image intensity imbalance through focus with alternating Phase Shift Masks (altPSMs) is performed and compared between a time-domain finite-difference (TDFD) algorithm (TEMPEST) and Geometrical theory of diffraction (GTD). Using GTD, with the solution to the canonical problems, we obtained a relationship between the edge on the mask and the disturbance in image space. The main interest is to develop useful formulations that can be readily applied to solve rigorous diffraction for future mask technology. Analysis of rigorous diffraction effects for altPSMs using GTD approach will be discussed.