Weighted Fit Alignment Curve for Lithographic Overlay Error Reduction
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Solution Overview
Problem
Conventional lithographic projection systems face challenges in achieving precise overlay control due to non-uniform sample distributions and fluctuations in data point spacing, leading to errors in alignment and focus positioning.
Innovation Solution
The implementation of a weighted fit method using transmission image sensors to determine the alignment curve, where measurements with denser samplings are given less weight than those with sparser samplings, producing a best fit curve that approximates the position of maximum radiation intensity, and a control system that adjusts machine parameters during the imaging process to improve overlay alignment.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional alignment methods are used with non-uniform sample distributions, then alignment measurements can be performed, but overlay errors increase due to non-uniform sampling and velocity fluctuations
Solution Approach 1:
The patent applies parameter changes by transforming the alignment measurement approach from direct sampling to polynomial curve fitting. The system collects alignment measurements at non-uniform intervals and uses polynomial interpolation to model the alignment curve, then derives alignment parameters (such as overlay correction values) from the fitted curve. This transformation allows the system to handle non-uniform sample distributions and velocity fluctuations by converting discrete, irregular measurements into a continuous, smooth alignment model, thereby improving manufacturing precision without sacrificing measurement capability.
2Ease of operation
If measurements are taken at regular intervals, then data processing is simplified, but velocity fluctuations cause non-uniform spacing and introduce fit errors
Solution Approach 1:
The patent applies dynamics by transitioning from static, evenly-spaced sampling to dynamic, adaptive polynomial fitting. The system continuously adjusts the polynomial order and fitting parameters based on the actual non-uniform spacing of measurements caused by velocity fluctuations. This dynamic approach allows the alignment model to adapt to changing measurement conditions, maintaining accuracy despite irregular sampling intervals and eliminating the need for rigid, uniform sampling requirements.
3Manufacturing precision
If polynomial fit order is increased to reduce fit error, then alignment accuracy improves, but computational complexity and risk of overfitting increase
Solution Approach 1:
The patent applies partial action by using a moderate polynomial fit order that provides sufficient accuracy without excessive complexity. Rather than using high-order polynomials that would perfectly fit all data points including noise, the system employs a balanced approach where the polynomial order is selected to capture the essential alignment trends while filtering out measurement noise. This partial fitting strategy achieves adequate alignment precision with manageable computational requirements and reduced overfitting risk.
Data Source
AI summary
A weighted fit based on a sample density of a plurality of samples is used to determine an alignment curve. A scan that produces the samples may include portions having greater and lesser sample density. While performing an interpolation to produce a best fit curve, a plurality of neighboring samples are chosen for each sample point, for sample points associated with a value above a threshold. A weighting function may be performed based on a distance between a given sample and the chosen nearest neighbors, wherein measurements that are taken in a region with denser samples are given less weight than measurements that are taken in a region with sparser samples.