Parametric Curve Layouts for Faster Computational Lithography
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Solution Overview
Problem
The increasing complexity of integrated circuit designs, with smaller and less rectilinear features, makes traditional polygon-based representations of lithographic shapes computationally intensive and difficult to simulate.
Innovation Solution
Representing lithographic layouts using parametric curves, such as cubic Bezier curves, to improve computational efficiency and reduce resource requirements.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If traditional polygon-based representations are used for lithographic shapes, then the representation is simple and intuitive, but the computational intensity increases and simulation becomes more difficult
Solution Approach 1:
The patent transforms the representation of lithographic shapes from polygon-based (discrete vertices and edges) to parametric curve-based (continuous mathematical functions). This parameter change allows the same geometric shapes to be described more efficiently, reducing computational intensity while maintaining representation accuracy. The parametric curves enable faster simulation by providing a more compact and mathematically tractable description of the shapes.
2Adaptability or versatility
If curvilinear shapes are used in mask designs, then the design flexibility increases, but the simulation difficulty increases when represented as polygons
Solution Approach 1:
The patent directly addresses curvilinear shapes by using parametric curves (such as B-splines or Bezier curves) to represent mask features. This approach naturally handles curves and complex geometries without requiring approximation by many small polygon segments. The parametric representation maintains design flexibility for curvilinear shapes while significantly reducing simulation difficulty compared to polygon-based representations.
3Manufacturing precision
If polygons with many vertices are used to approximate curved shapes, then the shape accuracy improves, but the computational intensity increases
Solution Approach 1:
The patent resolves this contradiction by changing the fundamental parameterization method from discrete polygon vertices to continuous parametric curves. A single parametric curve can represent a curved shape with high accuracy using far fewer parameters than would be required to approximate the same curve with many polygon vertices. This parameter change maintains shape accuracy while dramatically improving computational efficiency.
Data Source
AI summary
A layout is used in a computational lithography process. For example, the layout may be the layout of the lithographic mask or the layout of the desired resist shape. The layout is made up of multiple disjoint shapes. At least some of the disjoint shapes are represented by parametric curve representations, rather than polygons or other rectilinear representations. The parametric curve representations of the shapes are then used in the computational lithography process.