Illumination Optimization in Optical Projective Lithography

As lithography still pushing toward to lower k(1) imaging, traditional illumination source shapes may perform marginally in resolving complex layouts, freeform source shapes are expected to achieve better image quality. Illumination optimization as one of inverse lithography techniques attempts to synthesize the input source which leads to the desired output wafer pattern by inverting the forward model from mask to wafer. Usually, inverse lithography problem could be solved by standard numerical methods. Recently, a set of gradient-based numerical methods have been developed to solve the mask optimization problem based on Hopkins' approach. In this study, the same method is also applied to resolve the illumination optimization but based on Abbe imaging formulation for partially coherent illumination. Firstly we state a pixel-based source representation, and analyze the constraint condition for source intensity. Secondly, we propose an objective function which includes three aspects: image fidelity, source smoothness and discretization penalty. Image fidelity is to ensure that the image is as close to the given mask as possible. Source smoothness and discretization penalty are to decrease the source complexity. All of the three items could be described mathematically. Thirdly, we describe the detailed optimization flow, and present the advantages of using Abbe imaging formulation as calculation mode of light intensity. Finally, some simulations were done with initial conventional illumination for 90nm isolated, dense and elbow features separately. As a result, we get irregular dipole source shapes for isolated and dense pattern, and irregular quadrupole for elbow pattern. The results also show that our method could provide great improvements in both image fidelity and source complexity.