Edge-Based Optical Proximity Correction With Differentiable Gradients
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Solution Overview
Problem
Conventional optical proximity correction (OPC) methods, particularly pixel-based OPC, face challenges in masking complexity, increased defects, and higher costs, while edge-based OPC lacks flexibility and precision in segment movement and manufacturability.
Innovation Solution
A differentiable edge-based OPC mechanism that employs a mask rule-aware gradient-based optimization approach, utilizing CUDA-accelerated ray casting and a novel SRAF seed generation algorithm, to efficiently guide mask edge segment movement and optimize sub-resolution assist features, ensuring manufacturability and reducing manufacturing costs.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If pixel-based OPC (inverse lithography) is used, then manufacturing precision and flexibility are improved, but device complexity and manufacturing cost increase
Solution Approach 1:
The patent segments the mask pattern into edge-based representations rather than pixel-based representations. Each edge is represented as a separate entity with position and normal vector, allowing for more efficient optimization and easier constraint satisfaction while maintaining manufacturing precision.
Solution Approach 2:
The patent changes the fundamental parameters from pixel intensity values to edge geometric parameters (position, normal vector). This parameter transformation enables gradient-based optimization to directly manipulate edge positions, achieving precise control over pattern formation with reduced computational complexity.
2Manufacturing precision
If pixel-based OPC is used, then manufacturing precision is improved, but ease of manufacture deteriorates
Solution Approach 1:
By segmenting the mask into edge-based representations, the patent reduces the number of parameters that need to be optimized and constrained. This segmentation enables simpler mask fabrication processes while maintaining precise edge placement, directly addressing the ease of manufacture concern.
Solution Approach 2:
The patent implements a differentiable optimization framework that provides feedback on edge placement accuracy. This feedback mechanism allows for iterative refinement of edge positions, ensuring high manufacturing precision while simplifying the overall manufacturing process through automated optimization.
3Device complexity
If edge-based OPC is used, then device complexity is reduced, but manufacturing precision deteriorates
Solution Approach 1:
The patent transforms edge-based representations into a differentiable parameter space where edge positions and orientations are represented as continuous variables. This parameter change enables gradient-based optimization to achieve high manufacturing precision while maintaining the simplicity of edge-based representations.
Solution Approach 2:
The patent replaces traditional mechanical/conventional edge adjustment methods with a differentiable optimization system. This substitution enables precise control over edge placement through mathematical optimization, achieving high manufacturing precision without the complexity of conventional approaches.
4Ease of manufacture
If conventional edge-based OPC is used, then ease of manufacture is improved, but manufacturing precision deteriorates
Solution Approach 1:
The patent introduces a differentiable feedback mechanism that continuously monitors and adjusts edge positions based on placement accuracy. This feedback loop enables the system to maintain high manufacturing precision while preserving the cost-effectiveness of edge-based approaches by optimizing only the critical edge parameters.
Solution Approach 2:
The patent refines the edge parameters (position, normal vector) through differentiable optimization, transforming conventional edge-based methods into a high-precision approach. This parameter refinement enables simultaneous achievement of ease of manufacture and high manufacturing precision by optimizing the representation and adjustment of edges.
Data Source
AI summary
Lithography mask generation processes utilizing a forward process that decomposes a resist pattern into segments and rasterizes the segments into a mask pattern using ray casting, and a backward process that determines lithography gradients for edge movements that incorporate mask rule constraints and propagates the lithography gradients into gradients and velocities for the segments.