Lithographic Alignment Grid Using Orthogonal Basis Functions
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Solution Overview
Problem
Current alignment systems in lithographic processes face challenges in accurately positioning substrates due to substrate distortion and non-linear grid complexities, leading to unpredictable overlay errors and ineffective run-to-run control.
Innovation Solution
Implementing a grid based on orthogonal basis functions, such as Chebyshev polynomials and Fourier series, to measure and extrapolate positions on a substrate, allowing for accurate alignment and displacement calculations at points corresponding to the roots of these functions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If a non-linear grid is used to improve overlay accuracy, then measurement precision is improved, but device complexity increases and run-to-run control becomes ineffective
Solution Approach 1:
The patent transforms the grid model from a complex non-linear formulation to a simplified linear parameter representation. By expressing the grid as a linear combination of basis vectors with time-varying parameters, the system maintains measurement precision while enabling effective run-to-run control through parameter damping and monitoring.
Solution Approach 2:
The patent segments the complex non-linear grid transformation into a linear framework with separate basis vectors and parameter components. This segmentation allows independent control and monitoring of grid parameters while maintaining overall measurement accuracy.
2Device complexity
If substrate distortion is monitored using traditional linear grids, then device complexity is kept low, but measurement precision deteriorates due to inability to capture non-linear distortions
Solution Approach 1:
The patent introduces dynamic parameters that evolve over time to capture substrate distortion characteristics. The linear grid model incorporates time-varying parameters that adapt to changing substrate conditions, enabling accurate distortion measurement while maintaining computational simplicity.
Solution Approach 2:
The patent implements run-to-run feedback control by monitoring grid parameters and applying damping to prevent parameter drift. This feedback mechanism maintains measurement precision across multiple production runs while keeping the overall system complexity manageable.
Data Source
AI summary
A lithographic system includes a lithographic apparatus comprising a projection system which projects a patterned radiation beam onto a target portion of a substrate and an alignment system which measures the position of a feature of the pattern on the substrate at a number of locations over the substrate. A controller compares the measured positions with points on a grid of values and extrapolates values for intermediate positions on the substrate based on values of corresponding intermediate points on the grid, so as to provide an indication of the intermediate positions on the substrate and their displacements relative to the grid. The grid is based on at least one orthogonal basis function, the measurement on the substrate being performed at positions corresponding to the root values of the at least one orthogonal basis function.