Enhancing mask process correction on curvilinear data with Bézier curve representation

With the adoption of multi-beam mask writers (MBMW), complex curvilinear patterns have become increasingly prevalent due to their advantages, such as a larger process window on the wafer. However, from a Mask Data Preparation (MDP) point of view, curvilinear data poses challenges related to increased data volume and computational demands. To address these challenges, the Curvilinear Working Group has introduced a new MULTIGON record as an extension of the OASIS format. The MULTIGON record represents curvilinear data as a combination of parametric curves. Previous research demonstrated that our Mask Process Correction (MPC) flow achieved sufficient accuracy on curvilinear data represented in a Piecewise-Linear (PWL) format. However, when dealing with MULTIGON input, PWL-based MPC faces a trade-off between conversion accuracy to PWL and the number of vertices, impacting runtime and data volume. This paper focuses on applying Implicit Bézier curve representation in MPC without converting MULTIGON to PWL. We will review the capabilities of Bézier-based MPC for MULTIGON input in terms of computational performance, output data volume, and correction accuracy. Additionally, we will highlight the advantages of utilizing Bézier curve representation for MPC flow over conventional PWL-based curvilinear data.