Curvilinear Data Formats and the Impact on Mask-to-Wafer Fidelity

Abstract

The introduction of curvilinear mask data formats has enabled more accurate representation of complex shapes in advanced lithography. However, the increased data volume and figure density present challenges for efficient mask writing and downstream processing. This study investigates curvilinear data handling using Bezier and B-spline representations, focusing on data compression efficiency and the impact of format accuracy on wafer printing. A workflow was developed to convert piecewise design layouts into curvilinear data under varying “maximum allowable error (MAE)” constraints, followed by aerial image simulations to quantify design-, mask- and wafer-level root mean square errors (RMSE). Results show that wafer printing errors are consistently lower than real mask errors, creating a margin that allows for substantial data reduction without sacrificing lithographic fidelity. Cubic Bezier (CB) enables substantial data reduction while maintaining lower wafer error compared to real mask error, achieving higher compression efficiency than quadratic B-spline (QBS). These findings highlight the trade-off between data volume reduction and printing accuracy, and provide guidelines for selecting error thresholds based on process requirements. In addition, this study further verifies wafer printing simulations based on real mask contours, comparing them with simulations from the original design to further validate the effectiveness of curvilinear data handling methods.