Arbitrarily Polarized Illumination Source Modeling in Optical Lithography
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Solution Overview
Problem
Existing optical lithography models inadequately represent the complex polarization behavior of illumination sources, leading to inaccuracies in modeling and image formation during semiconductor manufacturing, especially as feature sizes decrease.
Innovation Solution
A system that models the polarization state of an illumination source by defining a polarization state vector at each grid point in a 2D grid map, decomposing it into unpolarized and completely polarized components, and applying separate transfer matrices for each component to enhance the lithography model.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If existing OPC models treat the illumination source as uniformly polarized light or unpolarized light, then the model complexity is low and ease of manufacture is improved, but the manufacturing precision and modeling accuracy deteriorate for smaller feature sizes
Solution Approach 1:
The illumination source pupil is divided into a two-dimensional grid map with multiple grid points. Each grid point is assigned an independent polarization state vector, allowing the model to capture spatial variations in polarization across the source without requiring a complete reformulation of the entire modeling framework. This segmentation enables accurate representation of complex polarization distributions while maintaining computational tractability.
Solution Approach 2:
Each grid point in the illumination source pupil is assigned a local polarization state that can differ from other grid points. This local quality approach allows the model to accurately represent the fact that different regions of the illumination source may have different polarization characteristics, thereby improving modeling accuracy for small features while keeping the overall model structure manageable.
2Device complexity
If existing OPC models treat the projection lens as a simple scalar lens pupil acting homogeneously, then the device complexity is low, but the reliability and accuracy of polarization state change modeling deteriorate
Solution Approach 1:
The projection lens pupil is segmented into multiple discrete points across its aperture. Each point is assigned a polarization transformation matrix that describes the local polarization effects. This segmentation allows the model to capture spatially varying polarization transformations through the lens without requiring a complete vectorial diffraction theory formulation, thus improving reliability while controlling complexity.
3Ease of operation
If existing OPC models use simplified polarization representations, then the ease of operation is improved, but the measurement precision and fidelity of polarization behavior deteriorate
Solution Approach 1:
The model uses polarization state vectors with four parameters (amplitude, phase, and two polarization components) at each grid point instead of simplified scalar representations. This parameter expansion enables accurate description of arbitrary polarization states including elliptical and circular polarization, while the modular grid-based structure maintains ease of operation by allowing independent specification of each grid point's polarization state.
Data Source
AI summary
One embodiment of the present invention provides a system that accurately models polarization states of an illumination source in an optical lithography system for manufacturing integrated circuits. During operation, the system starts by receiving a two-dimensional (2D) grid map for an illumination source pupil in the optical lithography system. The system then constructs a source-polarization model for the illumination source by defining a polarization state at each grid point in the grid map. Next, the system enhances a lithography model for the optical lithography system by incorporating the source-polarization model into the lithography/OPC model.