Curved Mask Layer Design Using Levelset Functions
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Solution Overview
Problem
Existing computational lithography tools struggle to efficiently handle and simulate curved mask features, as they are typically represented as polygons, leading to increased computational intensity and inaccuracies.
Innovation Solution
The use of levelset functions to represent and design curved mask layers, allowing for direct handling and modification of curved features through field representations, rather than polygon approximations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If curved mask features are represented as polygons, then existing computational lithography tools can process them, but computational intensity increases and accuracy decreases
Solution Approach 1:
The patent changes the fundamental parameter representation from polygon vertices to levelset function values. Instead of representing curved features as discrete polygon points, the levelset function uses continuous mathematical parameters (distance transforms, signed distance values) to represent the same geometric information, achieving both accuracy and computational efficiency
Solution Approach 2:
The patent substitutes the mechanical polygon approximation system with a mathematical field-based system. Rather than using discrete geometric primitives (polygons) to approximate curves, the system uses continuous levelset functions that naturally represent curved boundaries, eliminating the need for polygonal approximation and its associated computational overhead
2Ease of manufacture
If curved mask features are represented as polygons, then existing tools can handle them, but simulation and correction become more difficult
Solution Approach 1:
The patent transforms the representation parameters from discrete polygon coordinates to continuous levelset field values. This parameter transformation enables direct mathematical operations on curved features, making simulation and correction operations simpler and more intuitive compared to polygon manipulation
Solution Approach 2:
The levelset function representation provides a universal framework that handles both curved and straight features uniformly. The same levelset mathematical operations apply to all feature types, eliminating the need for special-case handling and simplifying the overall simulation and correction process
3Manufacturing precision
If polygon approximation is used for curved shapes, then computational lithography tools can process them, but edge placement accuracy decreases
Solution Approach 1:
The patent changes the representation from discrete polygon parameters to continuous levelset field parameters. This enables precise representation of curved boundaries without approximation errors, as the levelset function naturally captures the true geometry of curved features at any resolution
Data Source
AI summary
In some aspects, a lithographic mask having multiple features including a curved main feature is designed. A mask layer that represents a vector representation of the lithographic mask is first accessed. A correction field between a simulation field and a target field is then computed. The simulation field is a field representation of a simulated result of a lithography process using the lithographic mask, and the target field is a field representation of a target result of the lithography process. The main feature of a mask field is modified based on the correction field, where the mask field is a field representation of the main feature of the lithographic mask. Finally, the main feature of the mask layer is updated based on the modification to the mask field. This process can be repeated for multiple iterations, and, after the last iteration, a final version of the mask layer is output.