Regression Model Alignment for Substrate Measurement Accuracy
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Current exposure technologies face challenges in achieving high alignment accuracy for multiple layers on a substrate due to the tradeoff between measurement points and productivity, leading to overfitting and increased measurement time, especially with the need for higher-order components in miniaturized devices.
Innovation Solution
A method using a regression model with a prior distribution to estimate the array of regions on a substrate, where the parameters are updated based on posterior distributions from initial and subsequent position measurement data, allowing for accurate alignment with a smaller number of measurement points, thereby reducing overfitting and improving productivity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the number of measurement points is increased to suppress overfitting, then alignment accuracy is improved, but measurement time increases and productivity lowers
Solution Approach 1:
The patent applies preliminary action by using the alignment mark position data from the first substrate to estimate and establish a prior distribution for the regression model parameters before processing the second substrate. This prior distribution serves as a preliminary result that informs subsequent measurements, allowing the system to achieve accurate alignment with fewer measurement points on the second substrate while maintaining high productivity.
2Measurement precision
If the degree of freedom of the function model is increased to improve alignment accuracy, then correction accuracy of unmeasured regions is improved, but the number of measurement points required increases
Solution Approach 1:
The patent uses the prior distribution obtained from the first substrate as a preliminary foundation to guide the regression model analysis of the second substrate. This allows the system to employ high-order polynomial models with many degrees of freedom to accurately capture complex distortion patterns while requiring fewer measurement points, as the prior distribution provides initial constraints that reduce the information gap.
Solution Approach 2:
The patent applies copying by using the alignment mark position data from the first substrate as a template or reference to infer the prior distribution for the second substrate. This copied information allows the regression model to make accurate predictions about the second substrate's distortion characteristics without requiring exhaustive measurement of all regions, thus reducing the number of measurement points needed while maintaining high correction accuracy.
3Measurement precision
If alignment mark detection is performed for all regions on the substrate, then most accurate alignment is achieved, but productivity is reduced
Solution Approach 1:
The patent performs preliminary alignment mark detection on the first substrate to obtain position data that is used to establish a prior distribution. This prior distribution then serves as a foundation for accurately determining the alignment marks on the second substrate with fewer actual measurements, thereby achieving high alignment accuracy while maintaining high productivity by avoiding the need to measure all regions on every substrate.
Data Source
AI summary
The preset invention provides a method of obtaining an array of a plurality of regions on a substrate, including obtaining, using a prior distribution representing a probability distribution of parameters of a regression model used to estimate the array, a first posterior distribution representing the probability distribution of the parameters, obtaining, using the first posterior distribution as the prior distribution representing the probability distribution of the parameters, a second posterior distribution representing the probability distribution of the parameters, and updating the regression model by deciding the parameters based on the second posterior distribution and obtaining, using the updated regression model, the array of the plurality of regions on a substrate from the second position measurement data.