Coarse Mask Rendering with Pseudo Lens Subpixels

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Solution Overview

Problem

Current pixel-based image simulation methods for photolithography face challenges in accurately rendering mask features due to the high density of design gridding, leading to computational difficulties and inaccuracies in calculating SOCS images on fine grids, which results in errors in predicting printed feature edges and variations in rendering errors across different instances of a feature.

Innovation Solution

A method is introduced to render a mask as a coarse representation using a pseudo lens with a numerical aperture larger than the projection lens, allowing for a bandlimited Fourier transform that matches the mask, reducing computational overhead and improving accuracy by focusing on spatial frequencies within the bandlimit of the pseudo lens, and adjusting subpixels to accurately represent polygon fragments and edge fields.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Measurement precision

If pixel-based image simulation uses fine-gridded calculations to accurately represent mask features, then rendering precision is improved, but computational complexity and processing time increase significantly

Engineering Contradiction:
Improverendering precisionVSAvoidcomputational complexity
Core Design Contradiction:
Measurement precisionVSDevice complexity

Solution Approach 1:

The patent segments the mask rendering process into two distinct stages: (1) a coarse rendering stage using a lower-density grid to capture overall image characteristics, and (2) a fine rendering stage using a higher-density grid only for critical regions requiring precise edge representation. This segmentation allows the system to achieve accurate rendering where needed while avoiding the computational burden of applying fine-gridded calculations across the entire mask, thus resolving the contradiction between rendering precision and computational complexity.

Inventive Principle:
Principle #1Segmentation

Solution Approach 2:

The patent applies local quality by using transmission-matched subpixels with varying densities in different regions of the mask. Critical regions with important edge information use higher-density subpixel representations, while non-critical regions use lower-density representations. This localized approach ensures that rendering precision is improved only where necessary, rather than uniformly across the entire mask, thereby reducing overall computational complexity while maintaining accuracy for important features.

Inventive Principle:
Principle #3Local quality

2Productivity

If a coarse grid is used for initial rendering, then computational speed is improved, but accuracy in predicting printed feature edges deteriorates

Engineering Contradiction:
Improvecomputational speedVSAvoidedge prediction accuracy
Core Design Contradiction:
ProductivityVSMeasurement precision

Solution Approach 1:

The patent applies preliminary action by first performing a coarse rendering pass using a lower-density grid to quickly establish the overall image characteristics and identify critical regions. Based on this preliminary rendering, the system then selectively applies higher-density subpixel representations only to regions that require accurate edge prediction. This two-stage approach maintains computational speed by avoiding full fine-gridded rendering while still achieving the necessary edge prediction accuracy through targeted refinement.

Inventive Principle:
Principle #10Preliminary action

Solution Approach 2:

The patent introduces transmission-matched subpixels as an intermediary element that bridges the gap between coarse and fine rendering. These subpixels are strategically placed and sized to represent polygon fragments and edge fields, allowing the system to capture fine edge details without requiring a fully fine-gridded representation. The subpixels act as a mediator that enables accurate edge prediction while maintaining the computational efficiency of coarse-gridded rendering in non-critical regions.

Inventive Principle:
Principle #24Intermediary (Mediator)

3Manufacturing precision

If high-density subpixels are used to represent overhang portions, then rendering accuracy is improved, but computational overhead increases

Engineering Contradiction:
Improverendering accuracyVSAvoidcomputational overhead
Core Design Contradiction:
Manufacturing precisionVSUse of energy by stationary object

Solution Approach 1:

The patent applies local quality by using high-density transmission-matched subpixels only for overhang portions and critical edge regions, while using lower-density representations for other areas. The subpixel density is locally optimized based on the geometric complexity and importance of each region, ensuring that rendering accuracy is improved where it matters most (at overhangs and edges) without incurring the computational overhead of applying high-density subpixels uniformly across the entire mask.

Inventive Principle:
Principle #3Local quality

4Measurement precision

If the grid density is increased to reduce rendering errors, then prediction accuracy is improved, but processing time increases

Engineering Contradiction:
Improveprediction accuracyVSAvoidprocessing time
Core Design Contradiction:
Measurement precisionVSLoss of time

Solution Approach 1:

The patent segments the processing into stages of varying grid density, performing initial rendering with a coarse grid to quickly eliminate large errors, then selectively refining only critical regions with higher-density grids. This segmentation approach reduces the total number of fine-gridded calculations needed, thereby decreasing processing time while still achieving the necessary prediction accuracy for critical features.

Inventive Principle:
Principle #1Segmentation

Solution Approach 2:

The patent applies partial action by using high-density grid representations only for portions of the mask that require accurate prediction, rather than applying fine-gridded calculations to the entire mask. The transmission-matched subpixels are strategically placed to address the most critical regions, providing sufficient prediction accuracy without the excessive computational cost of uniform fine-gridded rendering across all areas.

Inventive Principle:
Principle #16Partial or excessive action

Applied Scientific Principles

This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.

Function Achieved in This Case

This approach enhances computational efficiency and accuracy by reducing the need for fine-gridded calculations, minimizing errors, and ensuring that the rendered mask closely resembles the true mask, while maintaining computational feasibility, thus improving the overall precision and speed of photolithographic simulations.

Implementation Method 1

A method is introduced to render a mask as a coarse representation using a pseudo lens with a numerical aperture larger than the projection lens, allowing for a bandlimited Fourier transform that matches the mask

Methodology Applied
Scientific EffectFourier transform:

Data Source

PatentUS8073288B2Rendering a mask using coarse mask representation
Publication Date: 2011.12.06 SIEMENS INDUSTRY SOFTWARE INC
  • US8073288B2 patent drawing
  • US8073288B2 patent drawing
  • US8073288B2 patent drawing

AI summary

A method, system and computer program product for rendering a mask are disclosed. A method of rendering a mask may comprise: providing an initial mask design for a photolithographic process, the initial mask design including polygons; initially rendering the initial mask design as a coarse mask representation in a pixel based image calculation; identifying an overhang portion; and rendering the overhang portion using a set of subpixels whose artifacts from spatial-localization lie outside a practical resolution of a pseudo lens having a numerical aperture larger than that of a projection lens used in the photolithographic process; and updating the initial rendering based on the overhang portion rendering.