Mask-Aware Lithography Modeling for Off-Axis Illumination
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Solution Overview
Problem
Current photolithography simulation methods, such as Abbe's and Hopkins' methods, are inefficient for full chip-level implementation due to computational complexity and inaccuracy when dealing with off-axis illumination and multi-tone masks, particularly in semiconductor manufacturing.
Innovation Solution
A novel integrated mask-aware lithography modeling scheme separates source-dependent information from mask geometry, transforming the light intensity calculation formula from Abbe's form to Hopkins' form using a transmission function matrix and convolution kernels, which are compressed using Eigen-kernels to maintain accuracy and speed.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If Abbe's method is used for photolithography simulation, then accuracy in light intensity calculation is improved, but computational speed deteriorates making it impractical for full chip level implementation
Solution Approach 1:
The patent segments the light source into multiple discrete points and processes each point individually through the mask function. This allows the computation to be divided into manageable segments that can be processed in parallel, maintaining Abbe's method accuracy while improving overall computational throughput for full chip simulations.
Solution Approach 2:
The patent pre-computes and stores the mask function in the frequency domain (Fourier transform of the mask) before the actual simulation. This preliminary action allows subsequent light intensity calculations to reuse the pre-computed mask data, significantly reducing the computational burden during full chip simulations while maintaining accuracy.
2Productivity
If Hopkins' method is used for photolithography simulation, then computational speed is improved, but accuracy deteriorates when dealing with off-axis illumination and multi-tone masks
Solution Approach 1:
The patent introduces an intermediary approach by using the frequency domain representation of the mask function as a bridge between Abbe's and Hopkins' methods. The mask's Fourier transform serves as a pre-computed intermediary that enables fast convolution-based calculations while accurately capturing off-axis illumination and multi-tone mask effects that Hopkins' method misses.
3Device complexity
If filter-based mask 3D modeling schemes are used, then computational effort is reduced, but accuracy deteriorates due to pattern dependency and fixed parameters that cannot adapt to off-axis illumination and multi-tone masks
Solution Approach 1:
The patent implements dynamic parameter adjustment where the mask transmission function is computed based on the actual mask geometry, off-axis illumination angles, and multi-tone characteristics. Unlike fixed filter-based parameters, the transmission function adapts dynamically to different patterns and illumination conditions, maintaining accuracy while managing computational complexity through efficient numerical methods.
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 reduces computational effort while maintaining high accuracy, achieving errors less than 1.6 nm critical dimension root mean square (RMS) compared to Abbe's method, and provides a practical solution for simulating photolithography processes involving off-axis illumination and multi-tone masks.
Implementation Method 1
image errors due to diffraction or process effects
Implementation Method 2
uses light to transfer a geometric pattern from an optical mask to a light-sensitive chemical
Data Source
AI summary
A method and apparatus of a novel modeling scheme for performing optical lithography simulation for a multi-tone mask with a plurality of mask tones is described. The method generates a transmission function matrix based on a setting of the multi-tone mask. The method applies the transmission function matrix to transform a formula for calculating light intensity from Abbe's form to Hopkins' form while maintaining the accuracy of Abbe's form. The method then computes the light intensity using the transformed formula.