Quantile Function Prediction Model for Edge Placement Error
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Solution Overview
Problem
Current metrology methods require extensive effort to monitor edge placement errors (EPE) across wafers due to their local and stochastic nature, necessitating dense measurement of feature instances at many locations, which is costly and time-consuming, especially in characterizing the tails of the distribution for accurate prediction.
Innovation Solution
A quantile function prediction model is developed to predict performance parameter distributions, specifically for edge placement errors, using a machine learning framework that fits a monotonic quantile function model to input distribution data, allowing for efficient prediction of quantile values across the substrate without the need for extensive measurement overhead.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If dense measurement of feature instances at many locations is performed to monitor edge placement errors, then measurement precision is improved, but measurement time and cost increase
Solution Approach 1:
The patent applies preliminary action by training a machine learning model on a large dataset of feature instances and locations beforehand. Once trained, the model can predict edge placement errors for new locations without requiring dense physical measurements. The training phase performs the computationally intensive work in advance, enabling fast predictions during actual monitoring operations.
Solution Approach 2:
The patent uses copying by creating a computational model that replicates the relationship between feature characteristics and edge placement errors based on training data. Instead of measuring every feature instance physically, the system copies the learned patterns from training examples to predict outcomes for new features, significantly reducing measurement requirements while maintaining accuracy.
2Measurement precision
If dense measurement of feature instances at many locations is performed to monitor edge placement errors, then measurement precision is improved, but manufacturing cost increases
Solution Approach 1:
The patent performs the expensive work of collecting and analyzing measurement data during a preliminary training phase. After training, the model can be deployed repeatedly at low marginal cost. The high upfront investment in training is amortized over many predictions, making the overall process more cost-effective than continuous dense measurements.
Solution Approach 2:
The patent creates a computational copy of the measurement and analysis process through the trained model. This digital twin can predict edge placement errors without requiring physical measurement equipment or expert analysis for each new feature, dramatically reducing per-unit manufacturing costs while maintaining measurement precision.
3Measurement precision
If extensive measurement overhead is used to characterize the tails of the distribution, then measurement precision is improved, but productivity decreases
Solution Approach 1:
The patent uses preliminary action by training the model on comprehensive datasets that include rare events and distribution tails during the offline training phase. Once trained, the model can predict tail behavior instantly without requiring additional measurements during production. The expensive characterization work is done in advance when productivity constraints are less severe.
Solution Approach 2:
The patent creates a computational representation of the distribution including its tails through the trained model. This model copy can generate predictions for extreme cases and tail regions without requiring actual measurements of rare events during production, maintaining statistical accuracy while enabling high throughput.
Data Source
AI summary
A method of determining a performance parameter distribution and/or associated quantile function. The method includes obtaining a quantile function prediction model operable to predict a quantile value for a substrate position and given quantile probability such that the predicted quantile values vary monotonically as a function of quantile probability and using the trained quantile 5 function prediction model to predict quantile values for a plurality of different quantile probabilities for one or more locations on the substrate.