Contrast-Source Inversion for Grating Profile Reconstruction
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Solution Overview
Problem
Current methods for reconstructing microscopic structures from electromagnetic scattering properties are computationally burdensome and impractical for real-time applications, especially when dealing with complex 2D-periodic structures, due to slow convergence and high computational costs in existing numerical methods like RCWA and VIM.
Innovation Solution
The use of a method that employs a continuous normal-vector field and a spectral discretization scheme with a heuristic approach to improve convergence, combined with a volume integral method and contrast-source inversion, to efficiently determine electromagnetic scattering properties and reconstruct structural parameters.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional numerical methods like RCWA and VIM are used to model electromagnetic scattering, then measurement precision can be achieved, but computational time and memory usage become excessively high
Solution Approach 1:
The patent transforms the electromagnetic scattering problem by changing the mathematical parameters and formulation approach. It introduces a volume integral equation formulation with a contrast current density that reformulates Maxwell's equations, enabling more efficient numerical solution while maintaining accuracy. This parameter transformation allows the problem to be solved with reduced computational complexity.
Solution Approach 2:
The patent replaces the conventional mechanical numerical methods (RCWA, VIM) with a contrast-source inversion approach based on volume integral equations. This substitution introduces a new mathematical framework that uses a contrast current density as the fundamental unknown, replacing the traditional field-based approaches and enabling faster convergence with lower computational cost.
2Measurement precision
If conventional numerical methods like RCWA and VIM are used to model electromagnetic scattering, then measurement precision can be achieved, but device complexity and computational resources increase
Solution Approach 1:
The patent reformulates the scattering problem by changing the fundamental parameters from field components to contrast current density. This parameter change simplifies the mathematical structure and reduces the complexity of the numerical implementation while maintaining measurement precision.
Solution Approach 2:
The patent extracts and isolates the scattering contrast into a separate contrast current density term. By taking out the material contrast properties and representing them as a distinct current density source, the problem becomes more tractable and reduces overall computational complexity.
3Manufacturing precision
If iterative reconstruction methods are used to match observed scattering data to physical structures, then manufacturing precision can be improved, but productivity decreases due to slow convergence
Solution Approach 1:
The patent changes the fundamental parameter being solved for from field distributions to contrast current density. This parameter transformation leads to faster converging iterative algorithms, improving both reconstruction accuracy and speed, thereby increasing productivity without sacrificing manufacturing precision.
Solution Approach 2:
The patent substitutes conventional iterative reconstruction algorithms with a contrast-source inversion method based on volume integral equations. This substitution replaces slow-converging traditional methods with a more efficient mathematical framework that achieves faster convergence and higher productivity.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach significantly reduces computational time and memory usage, achieving faster and more accurate reconstruction of microscopic structures by overcoming convergence issues and improving numerical efficiency.
Implementation Method 1
The model electromagnetic scattering property is determined using a volume integral method
Implementation Method 2
calculating electromagnetic scattering properties of a structure
Implementation Method 3
employing a spectral discretization scheme with a heuristic approach to improve convergence
Implementation Method 4
combined with a volume integral method and contrast-source inversion, to efficiently determine electromagnetic scattering properties and reconstruct structural parameters
Data Source
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AI summary
A CSI algorithm for reconstructing grating profiles is disclosed. Solving a volume integral equation for current density, J, employs the implicit construction of vector field, FS related to the electric field, ES, and current density, J, by selection of continuous components of E and J, F being continuous at one or more material boundaries, so as to determine an approximate solution of J. F is represented by at least one finite Fourier series with respect to at least one direction, x, y, and the step of numerically solving the volume integral equation comprises determining a component of J, by convolution of F, with a convolution operator, M comprising material and geometric structure properties in both directions. J may be represented by at least one finite Fourier series with respect to both directions. The continuous components can be extracted using convolution operators, PT and PN, acting on E and J.