Inverse lithography via polar representation for curvilinear mask synthesis

Abstract

BackgroundInverse lithography technology (ILT) revolutionized computational lithography by offering significant advantages over traditional optical proximity correction through its capacity for complex mask shapes and robust gradient-based optimization.AimWe aim to propose and analyze the impact of a polar mask representation on ILT performance, evaluating it against existing mask representations using various optimization algorithms.ApproachWe investigate the polar coordinate representation for mask shapes, expressing them as a series expansion in polar coordinates. Its performance is compared with polygonal, Bezier multigonal, and level set representations within ILT, measuring the efficiency of pre-conditioning and various first-order gradient descent methods.ResultsThe polar coordinate approach demonstrates superior performance, characterized by faster convergence and reduced data volume, all while maintaining high accuracy. These improvements are attributed to mathematical properties that naturally align with common lithographic patterns, particularly for contact and via layers.ConclusionsThe polar approach offers a high-performance framework for ILT, providing rapid convergence and a compact, efficient representation for smooth mask morphologies, beneficial for contact-like layers.