Thermal Aberration Prediction in Lithographic Projection Systems
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Solution Overview
Problem
Current projection systems in lithographic apparatuses face challenges in predicting and mitigating thermally induced aberrations, which lead to imaging property drift and productivity losses due to time-consuming wavefront sampling.
Innovation Solution
A method using a dynamic linear function to calculate temperature changes and a static non-linear function to predict thermally induced aberrations, allowing for accurate and cost-effective prediction and compensation of aberrations without the need for extensive wavefront sampling, utilizing a Wiener model with 5 estimated parameters.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If wavefront sampling is performed at substrate level to measure aberrations, then measurement precision is improved, but productivity deteriorates due to time consumption
Solution Approach 1:
The patent creates a computational model that replicates the complex physical measurement process. Instead of performing actual wavefront sampling at the substrate level, the system uses a model that copies the essential physics of thermal aberration generation and propagation, providing accurate predictions without the time cost of physical measurements
Solution Approach 2:
The patent performs preliminary computational work by developing and calibrating the aberration prediction model beforehand. Once calibrated, the model can quickly predict aberrations for different scenarios without requiring time-consuming wavefront sampling, enabling rapid compensation decisions
2Manufacturing precision
If complex thermal modeling is performed to accurately predict aberrations, then manufacturing precision is improved, but device complexity increases
Solution Approach 1:
The patent divides the thermal aberration prediction problem into two separate functional blocks: a dynamic linear function that handles time-dependent temperature evolution, and a static non-linear function that handles the relationship between temperature and optical aberrations. This segmentation allows each block to be optimized independently and simplifies the overall computational structure
Solution Approach 2:
The patent transforms the complex thermal-optical coupling problem into a parameter-based computational model. By using only 5 key parameters (amplitude, time constant, and three polynomial coefficients), the system captures the essential physics without requiring complex spatial and temporal simulations, significantly reducing computational complexity while maintaining accuracy
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 enables quick, accurate, and cost-effective prediction and compensation of thermally induced aberrations, reducing yield loss and avoiding the need for time-consuming wavefront sampling at the substrate level, while being applicable across different applications.
Implementation Method 1
During the projection of the pattern onto the substrate, the projection system will heat up, and this will cause the imaging properties of the projection system to drift
Implementation Method 2
The aberrations caused by the mirror heating depend on the application in the lithographic apparatus
Data Source
AI summary
A method of predicting thermally induced aberrations of a projection system for projecting a radiation beam, the method comprising: calculating a change in temperature of the projection system from a power of the radiation beam output from the projection system using a dynamic linear function; and calculating the thermally induced aberrations from the calculated change in temperature using a static non-linear function.