Lithography Model Using TCC Kernel Decomposition
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Solution Overview
Problem
The challenge in creating accurate masks for lithography processes lies in the distortions caused by higher order optical effects and increased pattern density, especially as feature sizes decrease below the diffraction limit, leading to unwanted features and variations in the lens pupil function, particularly in extreme ultraviolet (EUV) lithography.
Innovation Solution
The use of a single lithography model with an ideal Transmission Cross Coefficient (TCC) kernel set and perturbation kernel sets to account for position-dependent effects, reducing wafer edge placement errors and simplifying the computation process by representing the optical system with a product of ideal and perturbation kernels, which model the ideal optical system and its defects respectively.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If feature size decreases below the diffraction limit, then higher resolution is achieved, but distortions from higher order optical effects create unwanted features
Solution Approach 1:
The patent applies optical proximity correction (OPC) techniques to pre-compensate for optical distortions in the mask design before lithography. By calculating and adjusting the mask pattern in advance based on the optical system's point spread function, the unwanted diffraction effects are counteracted, allowing high-resolution features to be printed accurately without the harmful distortions that would otherwise occur at sub-diffraction limit dimensions.
2Productivity
If pattern density increases, then more features are printed, but intensity of light diffracted from neighboring patterns is no longer negligible
Solution Approach 1:
The patent implements location-dependent optical correction by dividing the mask into multiple regions and applying specific correction parameters to each region. The point spread function and its derivatives are calculated for different locations on the mask, allowing the system to account for varying diffraction conditions in high-density pattern areas. This local optimization ensures that neighboring patterns do not interfere with each other through unwanted light diffraction, maintaining pattern fidelity even at high densities.
3Manufacturing precision
If variation in lens pupil function across exposure slit is considered, then accuracy is improved, but computational complexity increases
Solution Approach 1:
The patent segments the optical system modeling into manageable components by calculating the point spread function and its spatial derivatives separately for different regions of the mask. The lens pupil function variation across the exposure slit is divided into multiple discrete location measurements, and correction parameters are computed for each segment. This segmentation approach maintains high lithography accuracy by accounting for local optical variations while reducing overall computational complexity through systematic decomposition of the problem.
4Measurement precision
If multiple lithography models are used for different mask locations, then position-dependent effects are captured, but device complexity increases
Solution Approach 1:
The patent creates a universal lithography model that can handle position-dependent effects through a single unified framework. By using the point spread function and its spatial derivatives in a general correction formulation, the model can be applied consistently across all mask locations without requiring separate models for each region. This universal approach captures position-dependent optical variations while maintaining model simplicity and reducing the complexity that would arise from managing multiple separate lithography models.
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 minimizes wafer edge placement errors, reduces computational complexity, and ensures consistent lithography models across the photomask, leading to improved imaging fidelity and reduced memory utilization.
Implementation Method 1
intensity of light diffracted from neighboring patterns
Data Source
AI summary
A method of making a mask includes computing a transmission cross coefficient (TCC) matrix for an optical system for performing a lithography process, wherein computing includes decomposing the transmission cross coefficient matrix into an ideal transmission cross coefficient (TCC) kernel set for a corresponding ideal optical system and at least one perturbation kernel set with coefficients corresponding to optical defects in the optical system, calibrating a lithography model by iteratively adjusting the lithography model based on a comparison between simulated wafer patterns and measured printed wafer patterns, and providing the calibrated lithography model, which includes an ideal TCC kernel set and the at least two perturbation kernels sets and a resist model, to a mask layout synthesis tool to obtain a synthesized mask layout corresponding to a target mask layout for manufacturing the mask using the synthesized mask layout.