Reticle Heating Model for Lithographic Overlay Correction
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Solution Overview
Problem
The increasing complexity of finite elements method (FEM) models in lithographic processes to account for reticle heating and cooling effects leads to high numerical efforts, making real-time adjustment of reticle positioning challenging, resulting in inadequate imaging performance due to thermal distortions.
Innovation Solution
A method involving the calibration of a linear time invariant reticle heating model using system identification, predicting distortions, and applying corrections based on these predictions to improve imaging performance by filtering noise and accounting for reticle heating and cooling effects.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If a finite elements method (FEM) model is used to model reticle heating effects, then imaging performance (overlay and focus) can be improved, but the complexity of the model increases and numerical effort increases
Solution Approach 1:
The patent creates a simplified copy of the complex FEM model by developing a reduced-order model that replicates the essential thermal behavior of the reticle. This reduced-order model uses pre-calculated influence matrices and superposition principles to approximate FEM results without requiring full FEM computational resources, thereby maintaining imaging performance correction capability while reducing model complexity.
Solution Approach 2:
The patent segments the thermal analysis into distinct components: influence matrices are pre-calculated for different heat source locations and patterns. By dividing the reticle into discrete regions with specific heat sources (e.g., illumination areas, cooling channels), the model can process thermal effects independently and combine results through superposition, reducing overall computational complexity.
2Manufacturing precision
If a complex FEM model is used to account for reticle cooling effects, then imaging performance can be improved, but the numerical effort increases making real-time adjustment challenging
Solution Approach 1:
The patent performs preliminary calculations by pre-computing influence matrices for various heat source configurations and cooling scenarios before actual lithographic exposure. These pre-calculated matrices are stored and reused during real-time operation, eliminating the need for complex FEM calculations during production. This allows real-time adjustment of reticle positioning to compensate for thermal effects while maintaining high calculation speed.
Solution Approach 2:
The patent creates a simplified computational copy of the thermal system that replicates FEM model behavior using pre-calculated influence matrices and linear superposition. This reduced-order model copy enables real-time thermal compensation calculations without requiring the full numerical effort of the original complex FEM model, thus improving productivity while maintaining correction accuracy.
3Measurement precision
If the FEM model complexity increases to account for both heating and cooling effects, then overlay and focus accuracy can be improved, but the calculation time increases
Solution Approach 1:
The patent performs all complex FEM calculations and model calibration in advance during system setup and reticle characterization phases. Influence matrices for different heat source locations, patterns, and cooling conditions are pre-computed and stored. During actual lithographic production, only simple matrix operations and superposition calculations are needed, dramatically reducing calculation time while maintaining overlay and focus accuracy.
Solution Approach 2:
The patent creates a reduced-order model copy that replicates the behavior of the complex FEM model using pre-calculated influence matrices. This copy enables rapid calculation of thermal distortions under various exposure and cooling conditions without requiring repeated full FEM simulations, thus achieving both high measurement precision for overlay correction and low calculation time for real-time application.
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 the numerical effort required to calculate reticle heating and cooling effects, enabling faster and more accurate adjustments to maintain optimal imaging performance, particularly in overlay and focus, by using a reticle heating model to predict and correct distortions in real-time.
Implementation Method 1
The dose of radiation that is received by the reticle causes heating of the reticle
Implementation Method 2
This heating causes thermal expansion and as a result the shape of the reticle may change
Implementation Method 3
there is a need to cool the reticle with a reticle cooling system to cool the reticle below a certain temperature
Data Source
AI summary
A method of reducing effects of reticle heating and/or cooling in a lithographic process, the method including calibrating a linear time invariant reticle heating model using a system identification method; predicting distortions of the reticle using the reticle heating model and inputs in the lithographic process; and calculating and applying a correction in the lithographic process on the basis of the predicted distortions of the reticle.