Fast Marching Method Binarization for Inverse Lithography Mask Patterns
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Solution Overview
Problem
As semiconductor manufacturing approaches smaller nodes, optical proximity correction (OPC) faces challenges in efficiently optimizing mask patterns due to increasing complexity and optical proximity effects, making it difficult to achieve high fidelity in substrate patterns.
Innovation Solution
The implementation of inverse lithography technology (ILT) and the fast marching method (FMM) to optimize mask patterns, where ILT optimizes mask images on a pixel level and FMM is used for efficient binarization of pixelated mask images to extract binary mask patterns, reducing the number of optimization variables and improving efficiency.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If optical proximity correction (OPC) is used to compensate for distortions and defects in substrate patterns, then manufacturing precision is improved, but device complexity increases due to the increasing complexity of mask patterns at smaller nodes
Solution Approach 1:
The patent applies inverse lithography technology (ILT) which inverts the traditional OPC approach. Instead of iteratively adjusting mask patterns to achieve desired substrate patterns (forward optimization), ILT directly computes the optimal mask pattern from the target substrate pattern using optimization algorithms. This inversion reduces the complexity of mask patterns while maintaining high substrate pattern fidelity at smaller nodes
Solution Approach 2:
The patent transforms the mask pattern representation from traditional geometric shapes to pixel-based grayscale images, allowing continuous parameter optimization. By representing mask patterns as arrays of pixels with varying transmission values, the system can optimize each pixel's dose independently, achieving high precision substrate patterns without increasing overall mask complexity
2Manufacturing precision
If inverse lithography technology (ILT) optimizes mask images on a pixel level, then manufacturing precision is improved, but computation time increases due to the large number of optimization variables
Solution Approach 1:
The patent segments the pixel-level optimization problem into multiple coarser resolution stages. The optimization process first works at a lower resolution to establish the overall pattern structure, then progressively refines at higher resolutions. This multi-resolution segmentation reduces the total number of optimization variables at each stage while maintaining the ability to achieve high precision in the final mask pattern
Solution Approach 2:
The patent performs preliminary optimization at coarser resolutions before proceeding to finer pixel-level optimization. By pre-establishing the general pattern structure and eliminating obvious errors at lower resolutions, the system reduces the complexity of the subsequent fine-tuning stage, thereby reducing overall computation time while maintaining optimization accuracy
3Productivity
If the fast marching method (FMM) is used for binarization of pixelated mask images, then productivity is improved through efficient computation, but measurement precision may be reduced compared to traditional binarization methods
Solution Approach 1:
The patent applies the fast marching method with locally adaptive thresholding, where the binarization threshold is adjusted based on local image characteristics such as gradient magnitude and curvature. This allows the binarization process to maintain high precision at critical edges and features while efficiently processing large areas of the mask image, balancing both productivity and measurement precision
Data Source
AI summary
Methods, apparatuses, and systems for determining a binary mask pattern from a pixelated mask pattern include: determining, by a processor, based on a fast marching method (FMM), arrival values for pixels of a portion of the pixelated mask pattern; determining the binary mask pattern based on the arrival values; and updating at least one of the arrival values based on a comparison between a design pattern corresponding to the pixelated mask pattern and a substrate pattern simulated based on the binary mask pattern.