Mask Bias Approximation via Pixel Interpolation

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Solution Overview

Problem

The existing mask optimization process for manufacturing integrated circuits is lengthy and inefficient due to the need for inverse dithering, which is computationally expensive and time-consuming, especially when incorporating mask bias into the optimization process.

Innovation Solution

The method involves approximating mask bias by interpolating neighboring pixels of a mask image using a predetermined value, such as a Taylor expansion, to directly add mask bias to the mask image without the need for inverse dithering, thereby simplifying the optimization process and reducing computational expense.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Manufacturing precision

If inverse dithering is used to incorporate mask bias into the optimization process, then manufacturing precision is improved, but productivity deteriorates due to the lengthy and computationally expensive process

Engineering Contradiction:

Improvemask optimization precisionVSAvoidoptimization process speed

Core Design Contradiction:

Manufacturing precisionVSProductivity

Solution Approach 1:

The patent changes the parameter representation from polygon-based to pixel-based mask images, enabling the use of interpolation operations instead of computationally expensive inverse dithering. This parameter transformation allows mask bias to be incorporated through simple pixel value modifications while maintaining optimization precision.

Inventive Principle:

Principle #35Parameter changes

Solution Approach 2:

The patent replaces the mechanical/computational process of inverse dithering with a mathematical interpolation approach. By using pixel intensity interpolation to represent mask bias effects, the system eliminates the need for iterative inverse dithering calculations, dramatically improving computational efficiency while preserving manufacturing precision.

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

2Manufacturing precision

If inverse dithering is performed to add mask bias, then manufacturing precision is improved, but loss of time increases due to the computationally expensive operation

Engineering Contradiction:

Improvemask bias accuracyVSAvoidcomputation time

Core Design Contradiction:

Manufacturing precisionVSLoss of time

Solution Approach 1:

The patent transforms the problem from polygon-based mask representation to pixel-based representation, enabling the use of efficient interpolation algorithms. This parameter change allows mask bias to be applied through straightforward pixel value adjustments rather than time-consuming inverse dithering operations, reducing computation time while maintaining precision.

Inventive Principle:

Principle #35Parameter changes

Solution Approach 2:

The patent uses simple pixel intensity values as disposable computational elements that can be quickly modified through interpolation. Instead of performing expensive inverse dithering calculations, the system uses lightweight pixel value modifications that are computationally inexpensive and can be rapidly executed, significantly reducing time loss.

Inventive Principle:

Principle #27Cheap short-living objects (Disposable)

Data Source

PatentUS10705420B2Mask bias approximation

Publication Date: 2020.07.07 ASML US LLC

AI summary

Directly biasing a mask image is disclosed. A method includes generating a mask image for the mask, biasing the mask image to obtain a biased mask image, and simulating the biased mask image to obtain a wafer image to be compared to the design pattern. Biasing the mask image includes updating at least one pixel of the mask image using an interpolation of neighboring pixels of the at least one pixel, the interpolation being dependent on a predetermined value.