Lithographic Projection Optics Tuning via TCC Lookup Tables
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Solution Overview
Problem
Current lithographic projection apparatuses face challenges in optimizing illumination sources and projection optics to achieve efficient and practical source-mask optimization, particularly in low k1 lithography, which requires extensive computational resources and time, and lacks comprehensive methods for integrating non-linear effects of projection optics in behavior matching/tuning.
Innovation Solution
A computationally-efficient method for optimizing lithographic projection apparatuses by simultaneously optimizing the source, mask, and projection optics using a cost function that includes non-linear effects, allowing for faster convergence and larger process windows, and enabling behavior matching with reference scanners.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If source-mask optimization is performed using conventional methods, then pattern projection accuracy is improved, but optimization time and computational resources increase significantly
Solution Approach 1:
The patent pre-calculates and stores transmission cross-coefficient (TCC) values and other optical parameters in lookup tables before the actual optimization process. This preliminary computation of complex optical models allows the optimization algorithm to quickly retrieve pre-computed values instead of calculating them in real-time, dramatically reducing optimization time while maintaining pattern projection accuracy
Solution Approach 2:
The optimization process is divided into separate stages: pre-computation of optical parameters (TCC, pupil functions) stored in lookup tables, and the actual optimization loop that retrieves these pre-computed values. This segmentation allows computationally intensive calculations to be performed once beforehand, separating them from the time-sensitive optimization process
2Adaptability or versatility
If comprehensive optimization including projection optics is performed, then process window is enlarged, but computational complexity increases
Solution Approach 1:
Pupil functions and optical parameters of the projection optics are pre-computed and stored in lookup tables before optimization begins. This allows the comprehensive optimization to include projection optics effects without proportionally increasing computational complexity during the actual optimization process
Solution Approach 2:
The patent uses lookup tables that contain pre-computed copies of complex optical parameters (TCC values, pupil functions) that can be quickly retrieved during optimization. These tabulated copies replace the need for real-time calculation of complex optical models, reducing computational complexity while maintaining comprehensive optimization capability
3Manufacturing precision
If low k1 lithography is used to achieve smaller feature dimensions, then manufacturing precision is improved, but optimization becomes more computationally intensive and time-consuming
Solution Approach 1:
For low k1 lithography applications, the patent pre-computes and stores the complex transmission cross-coefficient values and optical parameters in lookup tables before optimization. This preliminary action allows the computationally intensive low k1 optimization to proceed efficiently by retrieving pre-computed values rather than calculating them during optimization, thereby improving productivity while maintaining the precision required for small feature dimensions
Data Source
AI summary
Described herein are methods for matching the characteristics of a lithographic projection apparatus to a reference lithographic projection apparatus, where the matching includes optimizing projection optics characteristics. The projection optics can be used to shape wavefront in the lithographic projection apparatus. According to the embodiments herein, the methods can be accelerated by using linear fitting algorithm or using Taylor series expansion using partial derivatives of transmission cross coefficients (TCCs).