Optical Parametric Model Optimization via Statistical Hypothesis Testing

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Solution Overview

Problem

Existing scatterometry methods for optimizing optical parametric models are subjective and fail to effectively guard against the inclusion of insignificant parameters, lacking objective methods for determining when to terminate significance testing, leading to inconsistencies and increased costs in model generation and evaluation.

Innovation Solution

A quantitative method using statistical hypothesis testing with alpha spending or alpha investing rules to objectively determine which parameters to include in the model, preventing insignificant parameters from being added and ensuring proper model optimization through sequential testing and stopping conditions.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Adaptability or versatility

If subjective user assessment is used to determine model parameters, then flexibility in model selection is maintained, but consistency and objectivity of model optimization deteriorates

Engineering Contradiction:

Improveflexibility in model selectionVSAvoidconsistency of model optimization

Core Design Contradiction:

Adaptability or versatilityVSReliability

Solution Approach 1:

The patent replaces the mechanical (manual) process of subjective user assessment with an automated statistical hypothesis testing system. The system automatically evaluates whether to include parameters in the model based on objective statistical criteria (p-values, F-statistics), eliminating human subjectivity while maintaining the flexibility to handle complex model selection scenarios.

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

2Measurement precision

If manual review of chi-square metrics is performed, then qualitative assessment of model fit is possible, but time consumption and cost increase

Engineering Contradiction:

Improvequalitative assessment of model fitVSAvoidtime for model optimization

Core Design Contradiction:

Measurement precisionVSLoss of time

Solution Approach 1:

The system performs self-service by automatically executing the complete model optimization process without requiring manual intervention. It autonomously evaluates model fit metrics, performs statistical hypothesis testing, and determines parameter inclusion/exclusion based on predefined statistical criteria, thereby eliminating time-consuming manual review while maintaining assessment precision.

Inventive Principle:

Principle #25Self-service

Solution Approach 2:

The patent implements automated feedback loops where the system continuously monitors model fit metrics (chi-square, F-statistics, p-values) and automatically adjusts the model parameters based on statistical significance. This closed-loop feedback mechanism eliminates the need for manual iterative review, significantly reducing optimization time while maintaining rigorous assessment standards.

Inventive Principle:

Principle #23Feedback

3Measurement precision

If parameters are added to improve model fit, then accuracy of characterization increases, but risk of including insignificant parameters increases

Engineering Contradiction:

Improveaccuracy of characterizationVSAvoidnoise parameters in model

Core Design Contradiction:

Measurement precisionVSObject-generated harmful factors

Solution Approach 1:

The patent replaces manual judgment of parameter significance with automated statistical hypothesis testing. The system objectively evaluates whether each parameter provides statistically significant improvement in model fit using F-statistics and p-values, automatically filtering out insignificant parameters while maintaining accurate characterization of the diffracting structure.

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

4Manufacturing precision

If sequential parameter testing is performed without stopping conditions, then thorough model optimization is achieved, but computational resources and time increase

Engineering Contradiction:

Improvemodel optimization thoroughnessVSAvoidcomputational efficiency

Core Design Contradiction:

Manufacturing precisionVSProductivity

Solution Approach 1:

The patent implements feedback-based stopping conditions that automatically terminate the sequential parameter testing process when predefined criteria are met. The system monitors F-statistics, p-values, and model fit metrics in real-time and stops optimization when statistical significance thresholds are no longer met, preventing unnecessary computational resources from being expended on marginally significant parameters while maintaining thorough optimization.

Inventive Principle:

Principle #23Feedback

Data Source

PatentUS9435735B1Optical parametric model optimization

Publication Date: 2016.09.06 KLA CORP

AI summary

Provided are scatterometry model optimizations for evaluating a diffracting structure. In one embodiment, a method includes identifying one or more parameters to test for inclusion in the model. The method includes computing a difference between modeled data generated with the one or more parameters and measured data. The one or more parameters are included in the model in response to a reduction in the difference between the modeled data and the measured data compared to previous modeled, and passing a statistical hypothesis test. In one embodiment, the one or more parameters pass the statistical hypothesis test in response to the probability of obtaining the reduction in the difference is less than a significance level. In one embodiment, the significance level is a function of an alpha wealth value. In one embodiment, the method includes ordering the plurality of parameters for testing according to one or more criteria.