Regularized Regression Alignment for Exposure Subsystems
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Solution Overview
Problem
Current exposure methods face challenges in achieving high alignment accuracy for miniaturized devices due to the tradeoff between alignment precision and productivity, particularly when using a global alignment method with a limited number of measurement points, leading to overfitting and increased measurement time.
Innovation Solution
A method utilizing a regularized regression model with an L1 norm to estimate the array of regions on a substrate, where coefficients are calculated and filtered to prevent overfitting, allowing for accurate alignment with a small number of measurement points and a high-degree-of-freedom function model, by using a test substrate to optimize the model parameters and applying them to a second substrate.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If the number of measurement points to measure the positions of alignment marks is increased to suppress overfitting, then the reliability of alignment accuracy is improved, but the measurement time increases and productivity lowers
Solution Approach 1:
The patent applies preliminary action by pre-calculating the optimal subset of measurement points and their corresponding weights before actual alignment operations. The system performs offline optimization to determine which alignment marks should be measured and with what importance weights, so that during production, only these pre-selected points need to be measured, achieving high reliability without increasing measurement time.
Solution Approach 2:
The patent changes parameters by optimizing the importance weights assigned to different measurement points and selecting the optimal subset of points to measure. By adjusting these parameters (which measurement points to measure and with what weights), the system achieves the best alignment accuracy with the minimum number of measurements, resolving the contradiction between reliability and productivity.
2Manufacturing precision
If the degree of freedom of the function model is increased by using a higher-order component as the degree of the polynomial, then the manufacturing precision of region array prediction is improved, but overfitting occurs when the number of measurement points is small, increasing correction errors of unmeasured regions
Solution Approach 1:
The patent changes parameters by optimizing the importance weights for different measurement points and selecting the optimal subset of points. This parameter optimization allows the use of high-degree polynomial models (high degree of freedom) without overfitting, because the optimized weights and subset selection ensure that the model generalizes well to unmeasured regions, thereby improving manufacturing precision without increasing correction errors.
Solution Approach 2:
The patent applies preliminary action by pre-optimizing the function model parameters (importance weights and measurement point selection) before actual use. This offline optimization ensures that when high-degree polynomials are used, they are properly configured to avoid overfitting, allowing the system to achieve high manufacturing precision while maintaining reliability for unmeasured regions.
3Measurement precision
If alignment mark detection is performed for all regions on the substrate, then the alignment accuracy is improved, but the measurement time increases and productivity lowers
Solution Approach 1:
The patent applies the taking out principle by extracting only the essential measurement points from the complete set of alignment marks. Instead of measuring all alignment marks on the substrate, the system identifies and measures only the optimal subset of points that provide sufficient information for accurate alignment, thereby maintaining measurement precision while significantly reducing measurement time and improving productivity.
Solution Approach 2:
The patent applies partial action by measuring only a portion (optimal subset) of the alignment marks rather than all of them. The importance weight optimization determines which partial set of measurements is sufficient to achieve the required alignment accuracy, avoiding the excessive action of measuring all points and thus improving productivity while maintaining precision.
Data Source
AI summary
A method including calculating, using an objective function, which includes a regression model used to estimate an array of a plurality of regions on a substrate and a regularization term used to limit a value of a coefficient of the regression model, a value of each of a plurality of coefficients included in the regression model, with which the objective function becomes not more than a reference value, extracting, based on the calculated values, the coefficient having the value not less than a threshold value from the plurality of coefficients, and obtaining, using a regression model including only the extracted coefficient, an array of a plurality of regions on a substrate.