Neural Network Hermite Interpolator for Scatterometry
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Solution Overview
Problem
Current methods for characterizing grating parameters in scatterometry are slow and inefficient, particularly when solving the inverse grating diffraction problem, as they require extensive computation to analyze diffracted light measurements and estimate grating parameters accurately.
Innovation Solution
A neural network meta-model is trained using both spectral signal evaluations and derivative information across a parameter space, allowing for rapid generation of reference spectra and improved accuracy in characterizing grating parameters by incorporating derivative values into the training process, either through algebraic methods or optimization procedures.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If rigorous diffraction modeling algorithms (RCWA) are used to compute theoretical spectra, then measurement precision is improved, but productivity deteriorates due to very slow computation speed
Solution Approach 1:
The patent pre-computes theoretical spectra and stores them in a library before actual measurement analysis. This preliminary action allows the system to rapidly retrieve and compare pre-computed spectra during inverse diffraction problem solving, eliminating the need for slow real-time RCWA computations while maintaining measurement precision through accurate pre-computed reference data
Solution Approach 2:
The patent creates a library of copied theoretical spectra from rigorous diffraction modeling. Instead of repeatedly computing the same spectra during analysis, the system uses copies of pre-computed spectra stored in the library, dramatically improving computation speed while preserving the accuracy of the original rigorous models
2Measurement precision
If regression analysis is performed on diffracted light measurements to estimate parameters, then measurement precision is improved, but loss of time increases due to extensive computation requirements
Solution Approach 1:
The patent performs preliminary computation of theoretical spectra and stores them in a library before regression analysis is needed. This allows the regression analysis to compare measurements against pre-computed spectra rather than computing spectra during regression, significantly reducing analysis time while maintaining precision through accurate spectral comparisons
Solution Approach 2:
The patent introduces a spectral library as an intermediary between the rigorous diffraction models and the regression analysis. This library serves as a pre-computed reference that mediates between the slow but accurate RCWA computations and the fast but measurement-dependent regression analysis, enabling rapid parameter estimation without sacrificing accuracy
Data Source
AI summary
Generation of a meta-model for scatterometry analysis of a sample diffracting structure having unknown parameters. A training set comprising both a spectral signal evaluation and a derivative of the signal with respect to at least one parameter across a parameter space is rigorously computed. A neural network is trained with the training set to provide reference spectral information for a comparison to sample spectral information recorded from the sample diffracting structure. A neural network may be trained with derivative information using an algebraic method wherein a network bias vector is centered over both a primary sampling matrix and an auxiliary sampling matrix. The result of the algebraic method may be used for initializing neural network coefficients for training by optimization of the neural network weights, minimizing a difference between the actual signal and the modeled signal based on a objective function containing both function evaluations and derivatives.