Isotropic Field Perturbation for Lithographic EMF Modeling
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Solution Overview
Problem
Current lithographic simulation methods, particularly for optical proximity correction (OPC), face inefficiencies due to the need for separate simulations for orthogonal polarizations and the inability to accurately model electromagnetic field (EMF) effects in sub-wavelength scale mask features, leading to increased computational time and errors.
Innovation Solution
The introduction of an isotropic field perturbation to the thin mask approximation, which combines the electric field differences for both polarizations, allowing for a single simulation under unpolarized illumination and reducing the computational burden by representing electromagnetic effects as a weighted coherent combination of edge field perturbations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If separate simulations are performed for orthogonal polarizations to accurately model EMF effects, then modeling accuracy is improved, but computational time increases
Solution Approach 1:
The patent combines the electromagnetic field effects for orthogonal polarizations into a single unified simulation by introducing an isotropic field perturbation model. This model represents the combined effect of both polarizations simultaneously, eliminating the need for separate simulations while maintaining accuracy in modeling EMF effects for sub-wavelength mask features.
Solution Approach 2:
The isotropic field perturbation model serves as a universal correction that applies to both orthogonal polarization components. By developing a single model that captures the essential EMF effects for any polarization state, the patent enables one simulation to replace multiple simulations, improving computational efficiency without sacrificing modeling accuracy.
2Measurement precision
If rigorous EMF modeling methods like DDM or BL are used, then accuracy in modeling electromagnetic effects is improved, but execution time increases
Solution Approach 1:
The patent employs a simplified isotropic field perturbation model that acts as a computationally inexpensive approximation compared to rigorous methods like DDM or BL. This simplified model provides sufficient accuracy for OPC simulations while being significantly faster to execute, effectively replacing computationally intensive methods with a more efficient alternative that maintains adequate precision.
Solution Approach 2:
The patent changes the modeling approach by introducing an isotropic field perturbation parameterization that simplifies the complex electromagnetic field interactions. This parameter change transforms the problem from requiring complex rigorous solutions to using a simplified analytical correction, thereby improving execution speed while maintaining acceptable accuracy for the application.
3Productivity
If thin mask approximation is used without EMF corrections, then computational efficiency is improved, but accuracy in sub-wavelength feature modeling deteriorates
Solution Approach 1:
The patent applies local quality by introducing field perturbation corrections only at specific locations where EMF effects are most significant - namely at the edges and corners of sub-wavelength mask features. The isotropic field perturbation is applied locally to these critical regions while maintaining the overall simplicity of the thin mask approximation, thereby improving accuracy where needed without compromising computational efficiency across the entire mask.
Solution Approach 2:
The isotropic field perturbation acts as an intermediary correction term between the simple thin mask approximation and the complex rigorous EMF models. This intermediary model captures the essential EMF effects for sub-wavelength features without requiring the full complexity of rigorous methods, thus bridging the gap between computational efficiency and modeling accuracy.
Data Source
AI summary
Modeling of lithographic processes for use in the design of photomasks for the manufacture of semiconductor integrated circuits, and particularly to the modeling of the complex effects due to interaction of the illuminating light with the mask topography, is provided. An isofield perturbation to a thin mask representation of the mask is provided by determining, for the components of the illumination, differences between the electric field on a feature edge having finite thickness and on the corresponding feature edge of a thin mask representation. An isofield perturbation is obtained from a weighted coherent combination of the differences for each illumination polarization. The electric field of a mask having topographic edges is represented by combining a thin mask representation with the isofield perturbation applied to each edge of the mask.