Lithography Simulation via Multi-Sampling Angular Source Radiation
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Solution Overview
Problem
Current lithographic projection technologies face challenges in accurately simulating and optimizing the projection of sub-wavelength features due to the complexity of radiation interactions with patterning devices and substrates, leading to inaccuracies in edge placements and critical dimensions, especially at small feature sizes and high densities.
Innovation Solution
A computer-implemented method that determines partial images formed from radiation portions propagating along different directions and adds them incoherently to simulate an aerial image, allowing for the adjustment of patterning device and projection optics parameters to improve image fidelity, using a database for transmission functions and partial images to optimize the design layout.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If multiple-sampling of angular distribution is used to simulate aerial image, then manufacturing precision of sub-wavelength features is improved, but computational complexity increases
Solution Approach 1:
The angular distribution of source radiation is divided into multiple discrete sampling directions. Instead of treating the continuous angular distribution as a single entity, the simulation segments it into separate directional components (e.g., first direction, second direction, third direction), allowing each to be processed independently and then combined to form the complete aerial image.
Solution Approach 2:
The simulation transitions from a single-direction assumption to multi-directional sampling by adding the angular dimension as a discrete variable. This transforms the problem from evaluating radiation along one path to evaluating along multiple angular paths, capturing the angular distribution effects that influence sub-wavelength feature formation.
2Productivity
If single-direction assumption is used in simulation, then computational speed is maintained, but manufacturing precision of sub-wavelength features deteriorates
Solution Approach 1:
Instead of simulating all possible angular directions continuously, the method uses a partial set of discrete sampling directions that are sufficient to capture the essential angular distribution effects. This partial sampling approach maintains computational efficiency while improving accuracy compared to single-direction simulation.
3Measurement precision
If incoherent addition of partial images is performed, then accuracy of aerial image simulation is improved, but computational resources required increase
Solution Approach 1:
The aerial image is segmented into multiple partial images, each corresponding to a specific sampling direction of the source radiation. Each partial image is calculated separately based on its directional component, and then these partial images are incoherently added together to produce the final aerial image, accurately representing the superposition of radiation from different angles.
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 accuracy of simulating and optimizing lithographic processes, improving edge placements and critical dimensions, and expanding the process window for sub-wavelength feature projection, thereby addressing the limitations of single-direction assumptions in existing simulations.
Implementation Method 1
a first radiation portion propagating along a first group of one or more directions from an illumination source and impinging on a patterning device
Implementation Method 2
determining an aerial image by adding incoherently the first partial image and the second partial image
Data Source
AI summary
A method including: determining a first simulated partial image formed, by a lithographic projection apparatus, from a first radiation portion propagating along a first group of one or more directions; determining a second simulated partial image formed, by the lithographic projection apparatus, from a second radiation portion propagating along a second group of one or more directions; and determining an image by incoherently adding the first partial image and the second partial image, wherein the first group of one or more directions and the second group of one or more directions are different.