Projection System Model Optimization for Lithographic Aberrations
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Solution Overview
Problem
Lithographic apparatuses face challenges in accurately adjusting optical elements to minimize optical aberrations and improve projection system performance, as existing methods are limited in effectively addressing complex aberrations and variations between optical elements.
Innovation Solution
A computer-implemented method using an evolutionary algorithm to optimize projection system models by generating and evaluating merit functions, allowing for adjustments in optical elements based on Zernike polynomials and Tikhonov variables, which helps in reducing residual optical aberrations and improving projection system characteristics.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If existing projection system modelling methods are used to adjust optical elements, then the system can reduce some optical aberrations, but the method is limited in effectively addressing complex aberrations and variations between optical elements
Solution Approach 1:
The patent applies parameter changes by systematically varying merit function parameters and weights through optimization algorithms. The method changes the parameters of the projection system model, including merit function weights and Zernike polynomial coefficients, to achieve better optimization results for complex optical aberrations and inter-element variations.
2Ease of operation
If a fixed merit function is used in the projection system model, then the model execution is simple, but the model cannot effectively adapt to different projection system characteristics and optimization scenarios
Solution Approach 1:
The patent implements dynamics by making the merit function adaptive rather than fixed. The optimization algorithm dynamically adjusts merit function weights and parameters based on projection system characteristics, allowing the model to adapt to different scenarios while maintaining automated execution through iterative optimization processes.
Solution Approach 2:
The patent applies feedback by using optimization algorithms that evaluate projection system characteristics and adjust merit function parameters accordingly. The system receives feedback from model execution results and uses this information to refine the merit function weights and parameters in subsequent iterations, improving adaptability while maintaining operational simplicity.
3Productivity
If traditional optimization methods are used to determine optical element adjustments, then the process is computationally efficient, but the methods cannot thoroughly search the complex solution space to find optimal parameters and weights
Solution Approach 1:
The patent introduces an intermediary optimization algorithm that bridges computational efficiency and optimization accuracy. The algorithm acts as a mediator by using surrogate models and intelligent search strategies to explore the complex solution space more thoroughly than traditional methods, achieving better precision while maintaining reasonable computational efficiency through automated parameter optimization.
Data Source
AI summary
A projection system model is configured to predict optical aberrations of a projection system based upon a set of projection system characteristics and to determine and output a set of optical element adjustments based upon a merit function. The merit function comprises a set of parameters and corresponding weights. The method comprises receiving an initial merit function and executing an optimization algorithm to determine a second merit function. The optimization algorithm scores different merit functions based upon projection system characteristics of a projection system adjusted according to the output of the projection system model using a merit function having that set of parameters and weights.