Piecewise Polynomial PSF for Electron Beam Proximity Correction
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Solution Overview
Problem
Conventional Gaussian-based Point Spread Functions (PSF) used in electron beam lithography and microscopy exhibit significant deviations between predicted and measured energy distributions, limiting the precision of electron beam interaction modeling and correction of scattering effects.
Innovation Solution
A method utilizing a piecewise polynomial PSF with radial variation, specifically a natural cubic spline, is employed to optimize the interpolation of scattering effects, allowing for precise correction of electron beam dose distribution and geometry, thereby improving the accuracy of electron beam projection and analysis.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If a conventional Gaussian-based PSF function is used to model electron scattering, then the modeling process is simple and computationally efficient, but the precision of energy distribution prediction deviates significantly from experimental measurements and Monte-Carlo simulations
Solution Approach 1:
The patent changes the functional form of the PSF from a Gaussian function to a piecewise polynomial function with adjustable parameters. This allows the model to better fit experimental data while maintaining computational efficiency. The piecewise polynomial structure enables flexible parameter adjustment to match the complex physics of electron scattering without requiring complex computational methods.
Solution Approach 2:
The patent divides the continuous PSF function into multiple polynomial segments that can be independently optimized. This segmentation allows for better local fitting of the energy distribution at different radial distances from the beam impact point, improving overall prediction accuracy while keeping each segment computationally simple.
2Measurement precision
If a PSF function with multiple Gaussians and negative weighting coefficients is used to improve scattering correction, then the modeling precision increases, but the device complexity and computational burden increase significantly
Solution Approach 1:
The patent changes from using multiple Gaussian functions with negative coefficients to a piecewise polynomial function with positive coefficients only. This parameter change simplifies the mathematical structure while maintaining the ability to accurately model the scattering distribution. The piecewise polynomial form avoids the complexity of negative weighting coefficients and multiple Gaussian components.
Solution Approach 2:
The patent uses a computationally inexpensive piecewise polynomial function that can be rapidly evaluated, replacing the more complex multi-Gaussian model. This 'simpler' model achieves comparable or better accuracy with significantly reduced computational burden, making it suitable for real-time or iterative applications.
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 enhances the precision of electron beam lithography and microscopy by reducing errors in dose distribution and pattern fidelity, offering a more realistic and efficient modeling of electron beam interactions with targets.
Implementation Method 1
Proximity effects are generated by forward scattering and back scattering of the electrons around the initial path
Implementation Method 2
Proximity effects are generated by forward scattering and back scattering of the electrons around the initial path
Data Source
AI summary
A method for projecting an electron beam onto a target includes correction of the scattering effects of the electrons in the target. This correction is made possible by a calculation step of a point spread function having a radial variation according to a piecewise polynomial function.